Optimized placement of vibration damper tools through mode-shape tuning

ABSTRACT

Systems and methods for damping torsional oscillations of downhole systems are described. The systems include a downhole drilling system disposed at an end of the downhole system in operative connection with a drill bit. A damping system is installed on the downhole drilling system, the damping system having at least one damper element configured to dampen at least one HFTO mode. At least one mode-shape tuning element is arranged on the drilling system. The at least one mode-shape tuning element is configured and positioned on the drilling system to modify at least one of a shape of the HFTO mode, a frequency of the HFTO mode, an excitability of the HFTO mode, and a damping efficiency of the at least one damper element.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Application Ser.No. 62/899,354, filed Sep. 12, 2019, U.S. Provisional Application Ser.No. 62/899,291, filed Sep. 12, 2019, U.S. Provisional Application Ser.No. 62/899,331, filed Sep. 12, 2019, and U.S. Provisional ApplicationSer. No. 62/899,332, filed Sep. 12, 2019, the entire disclosures ofwhich are incorporated herein by reference.

BACKGROUND 1. Field of the Invention

The present invention generally relates to downhole operations andsystems for damping vibrations of the downhole systems during operation.

2. Description of the Related Art

Boreholes are drilled deep into the earth for many applications such ascarbon dioxide sequestration, geothermal production, and hydrocarbonexploration and production. In all of the applications, the boreholesare drilled such that they pass through or allow access to a material(e.g., a gas or fluid) contained in a formation (e.g., a compartment)located below the earth's surface. Different types of tools andinstruments may be disposed in the boreholes to perform various tasksand measurements.

In operation, the downhole components may be subject to vibrations thatcan impact operational efficiencies. For example, severe vibrations indrillstrings and bottomhole assemblies can be caused by cutting forcesat the drill bit or mass imbalances in downhole tools such as mudmotors. Impacts from such vibrations can include, but are not limitedto, reduced rate of penetration, reduced quality of measurements, andexcess fatigue and wear on downhole components, tools, and/or devices.

SUMMARY

Disclosed herein are systems and methods for damping oscillations, suchas torsional oscillations, of downhole systems. The systems include adownhole system arranged to rotate within a borehole and a dampingsystem configured on the downhole system. The damping system includesone or more dampers that is installed at or in a drill bit or otherdisintegration device of the downhole system. The dampers are arrangedto reduce or eliminate one or more specific vibration modes, and thusimproved downhole operations and/or efficiencies may be achieved.

According to some embodiments, systems for damping torsionaloscillations of downhole systems are provided. The systems include adrilling system comprising a bottomhole assembly disposed on the end ofa drill string, at least one mode-shape tuning element arranged on thedrilling system, the at least one mode-shape tuning element configuredto shift the location of a maxima of a high-frequency torsionaloscillations (HFTO) mode, and a damping system configured on thedrilling system, the damping system comprising at least one damperelement arranged at the shifted location of the maxima.

According to some embodiments, methods of damping torsional oscillationsof a downhole system in a borehole are provided. The methods includeinstalling at least one mode-shape tuning element on a drilling system,the drilling system comprising a drill string and a bottomhole assembly,the at least one mode-shape tuning element configured to shift thelocation of a maxima of a high-frequency torsional oscillations (HFTO)mode of the drilling system and installing a damping system on thedrilling system, the damping system comprising at least one damperelement arranged at the shifted location of the maxima.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter, which is regarded as the invention, is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other features and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings, wherein like elements arenumbered alike, in which:

FIG. 1 is an example of a system for performing downhole operations thatcan employ embodiments of the present disclosure;

FIG. 2 is an illustrative plot of a typical curve of frictional force ortorque versus relative velocity or relative rotational speed between twointeracting bodies;

FIG. 3 is a hysteresis plot of a friction force versus displacement fora positive relative mean velocity with additional small velocityfluctuations;

FIG. 4 is a plot of friction force, relative velocity, and a product ofboth versus. time for a positive relative mean velocity with additionalsmall velocity fluctuations;

FIG. 5 is a hysteresis plot of a friction force versus displacement fora relative mean velocity of zero with additional small velocityfluctuations;

FIG. 6 is a plot of friction force, relative velocity, and a product ofboth for a relative mean velocity of zero with additional small velocityfluctuations;

FIG. 7 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 8A is a plot of tangential acceleration measured at a drill bit;

FIG. 8B is a plot corresponding to FIG. 8A illustrating rotary speed;

FIG. 9A is a schematic plot of a downhole system illustrating a shape ofa downhole system as a function of distance-from-bit;

FIG. 9B illustrates example corresponding mode shapes of torsionalvibrations that may be excited during operation of the downhole systemof FIG. 9A;

FIG. 10 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 11 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 12 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 13 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 14 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 15 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 16 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 17 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 18 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure;

FIG. 19 is a schematic illustration of a damping system in accordancewith an embodiment of the present disclosure; and

FIG. 20 is a schematic plot of a modal damping ratio versus localvibration amplitude;

FIG. 21 is a schematic illustration of a downhole tool having a dampingsystem;

FIG. 22 is a cross-sectional illustration of the downhole tool of FIG.21 ;

FIG. 23 is a set of plots illustrating mode shapes of various BHA modesand normalized damping for a damper in accordance with an embodiment ofthe present disclosure;

FIGS. 24A-24C are schematic illustrations of the placement of a singledamper element on a downhole in accordance with embodiments of thepresent disclosure;

FIG. 25 is a set of plots illustrating mode shapes of various BHA modesand normalized damping for a damper in accordance with an embodiment ofthe present disclosure;

FIG. 26A is a schematic illustration of a downhole string havingmode-shape tuning elements and a damper element installed thereon inaccordance with an embodiment of the present disclosure;

FIG. 26B illustrates modified or tuned mode shapes by incorporation ofmode-shape tuning elements in accordance with an embodiment of thepresent disclosure;

FIG. 27 is a schematic illustration of a tangential damper element inaccordance with an embodiment of the present disclosure;

FIG. 28 is a schematic illustration of a tangential damper element inaccordance with an embodiment of the present disclosure;

FIG. 29A is a schematic illustration of examples of mode-shape tuningelements in accordance with an embodiment of the present disclosure; and

FIG. 29B is a schematic illustration of an example assembly downholestring having mode-shape tuning elements and a damper element sub inaccordance with an embodiment of the present disclosure.

DETAILED DESCRIPTION

FIG. 1 shows a schematic diagram of a system for performing downholeoperations. As shown, the system is a drilling system 10 that includes adrill string 20 having a drilling assembly 90, also referred to as abottomhole assembly (BHA), conveyed in a borehole 26 penetrating anearth formation 60. The drilling system 10 includes a conventionalderrick 11 erected on a floor 12 that supports a rotary table 14 that isrotated by a prime mover, such as an electric motor (not shown), at adesired rotational speed. The drill string 20 includes a drillingtubular 22, such as a drill pipe, extending downward from the rotarytable 14 into the borehole 26. A disintegration device 50, such as adrill bit (also referred to as “bit”) attached to the end of the BHA 90,disintegrates the geological formations when it is rotated to drill theborehole 26. The drill string 20 is coupled to surface equipment such assystems for lifting, rotating, and/or pushing, including, but notlimited to, a drawworks 30 via a kelly joint 21, swivel 28 and line 29through a pulley 23. In some embodiments, the surface equipment mayinclude a top drive (not shown). During the drilling operations, thedrawworks 30 is operated to control the weight on bit, which affects therate of penetration. The operation of the drawworks 30 is well known inthe art and is thus not described in detail herein.

During drilling operations, a suitable drilling fluid 31 (also referredto as the “mud”) from a source or mud pit 32 is circulated underpressure through the drill string 20 by a mud pump 34. The drillingfluid 31 passes into the drill string 20 via a desurger 36, fluid line38 and the kelly joint 21. The drilling fluid 31 is discharged at theborehole bottom 51 through an opening in the disintegration device 50.The drilling fluid 31 circulates uphole through the annular space 27between the drill string 20 and the borehole 26 and returns to the mudpit 32 via a return line 35. A sensor S1 in the fluid line 38 providesinformation about the fluid flow rate. A surface torque sensor S2 and asensor S3 associated with the drill string 20 respectively provideinformation about the torque and the rotational speed of the drillstring. Additionally, one or more sensors (not shown) associated withline 29 are used to provide the hook load of the drill string 20 andabout other desired parameters relating to the drilling of the borehole26. The system may further include one or more downhole sensors 70located on the drill string 20 and/or the BHA 90.

In some applications the disintegration device 50 is rotated by onlyrotating the drill pipe 22. However, in other applications, a drillingmotor 55 (for example, a mud motor) disposed in the drilling assembly 90is used to rotate the disintegration device 50 and/or to superimpose orsupplement the rotation of the drill string 20. In either case, the rateof penetration (ROP) of the disintegration device 50 into the earthformation 60 for a given formation and a given drilling assembly largelydepends upon the weight on bit and the drill bit rotational speed. Inone aspect of the embodiment of FIG. 1 , the drilling motor 55 iscoupled to the disintegration device 50 via a drive shaft (not shown)disposed in a bearing assembly 57. The drilling motor 55 rotates thedisintegration device 50 when the drilling fluid 31 passes through thedrilling motor 55 under pressure. The bearing assembly 57 supports theradial and axial forces of the disintegration device 50, the downthrustof the drilling motor and the reactive upward loading from the appliedweight on bit. Stabilizers 58 coupled to the bearing assembly 57 and/orother suitable locations act as centralizers for the drilling assembly90 or portions thereof.

A surface control unit 40 receives signals from the downhole sensors 70and devices via a transducer 43, such as a pressure transducer, placedin the fluid line 38 as well as from sensors S1, S2, S3, hook loadsensors, RPM sensors, torque sensors, and any other sensors used in thesystem and processes such signals according to programmed instructionsprovided to the surface control unit 40. The surface control unit 40displays desired drilling parameters and other information on adisplay/monitor 42 for use by an operator at the rig site to control thedrilling operations. The surface control unit 40 contains a computer,memory for storing data, computer programs, models and algorithmsaccessible to a processor in the computer, a recorder, such as tapeunit, memory unit, etc. for recording data and other peripherals. Thesurface control unit 40 also may include simulation models for use bythe computer to processes data according to programmed instructions. Thecontrol unit responds to user commands entered through a suitabledevice, such as a keyboard. The surface control unit 40 is adapted toactivate alarms 44 when certain unsafe or undesirable operatingconditions occur.

The drilling assembly 90 also contains other sensors and devices ortools for providing a variety of measurements relating to the formationsurrounding the borehole and for drilling the borehole 26 along adesired path. Such devices may include a device for measuring theformation resistivity near and/or in front of the drill bit, a gamma raydevice for measuring the formation gamma ray intensity and devices fordetermining the inclination, azimuth and position of the drill string. Aformation resistivity tool 64, made according an embodiment describedherein may be coupled at any suitable location, including above a lowerkick-off subassembly 62, for estimating or determining the resistivityof the formation near or in front of the disintegration device 50 or atother suitable locations. An inclinometer 74 and a gamma ray device 76may be suitably placed for respectively determining the inclination ofthe BHA and the formation gamma ray intensity. Any suitable inclinometerand gamma ray device may be utilized. In addition, an azimuth device(not shown), such as a magnetometer or a gyroscopic device, may beutilized to determine the drill string azimuth. Such devices are knownin the art and therefore are not described in detail herein. In theabove-described exemplary configuration, the drilling motor 55 transferspower to the disintegration device 50 via a shaft that also enables thedrilling fluid to pass from the drilling motor 55 to the disintegrationdevice 50. In an alternative embodiment of the drill string 20, thedrilling motor 55 may be coupled below the resistivity measuring device64 or at any other suitable place.

Still referring to FIG. 1 , other logging-while-drilling (LWD) devices(generally denoted herein by numeral 77), such as devices for measuringformation porosity, permeability, density, rock properties, fluidproperties, etc. may be placed at suitable locations in the drillingassembly 90 for providing information useful for evaluating thesubsurface formations along borehole 26. Such devices may include, butare not limited to, temperature measurement tools, pressure measurementtools, borehole diameter measuring tools (e.g., a caliper), acoustictools, nuclear tools, nuclear magnetic resonance tools and formationtesting and sampling tools.

The above-noted devices transmit data to a downhole telemetry system 72,which in turn transmits the received data uphole to the surface controlunit 40. The downhole telemetry system 72 also receives signals and datafrom the surface control unit 40 and transmits such received signals anddata to the appropriate downhole devices. In one aspect, a mud pulsetelemetry system may be used to communicate data between the downholesensors 70 and devices and the surface equipment during drillingoperations. A transducer 43 placed in the fluid line 38 (e.g., mudsupply line) detects the mud pulses responsive to the data transmittedby the downhole telemetry system 72. Transducer 43 generates electricalsignals in response to the mud pressure variations and transmits suchsignals via a conductor 45 to the surface control unit 40. In otheraspects, any other suitable telemetry system may be used for two-waydata communication (e.g., downlink and uplink) between the surface andthe BHA 90, including but not limited to, an acoustic telemetry system,an electro-magnetic telemetry system, an optical telemetry system, awired pipe telemetry system which may utilize wireless couplers orrepeaters in the drill string or the borehole. The wired pipe telemetrysystem may be made up by joining drill pipe sections, wherein each pipesection includes a data communication link, such as a wire, that runsalong the pipe. The data connection between the pipe sections may bemade by any suitable method, including but not limited to, hardelectrical or optical connections, induction, capacitive, resonantcoupling, such as electromagnetic resonant coupling, or directionalcoupling methods. In case a coiled-tubing is used as the drill pipe 22,the data communication link may be run along a side of thecoiled-tubing.

The drilling system described thus far relates to those drilling systemsthat utilize a drill pipe to convey the drilling assembly 90 into theborehole 26, wherein the weight on bit is controlled from the surface,typically by controlling the operation of the drawworks. However, alarge number of the current drilling systems, especially for drillinghighly deviated and horizontal boreholes, utilize coiled-tubing forconveying the drilling assembly downhole. In such application a thrusteris sometimes deployed in the drill string to provide the desired forceon the drill bit. Also, when coiled-tubing is utilized, the tubing isnot rotated by a rotary table but instead it is injected into theborehole by a suitable injector while the downhole motor, such asdrilling motor 55, rotates the disintegration device 50. For offshoredrilling, an offshore rig or a vessel is used to support the drillingequipment, including the drill string.

Still referring to FIG. 1 , a resistivity tool 64 may be provided thatincludes, for example, a plurality of antennas including, for example,transmitters 66 a or 66 b and/or receivers 68 a or 68 b. Resistivity canbe one formation property that is of interest in making drillingdecisions. Those of skill in the art will appreciate that otherformation property tools can be employed with or in place of theresistivity tool 64.

Liner drilling can be one configuration or operation used for providinga disintegration device becomes more and more attractive in the oil andgas industry as it has several advantages compared to conventionaldrilling. One example of such configuration is shown and described incommonly owned U.S. Pat. No. 9,004,195, entitled “Apparatus and Methodfor Drilling a Borehole, Setting a Liner and Cementing the BoreholeDuring a Single Trip,” which is incorporated herein by reference in itsentirety. Importantly, despite a relatively low rate of penetration, thetime of getting the liner to target is reduced because the liner is runin-hole while drilling the borehole simultaneously. This may bebeneficial in swelling formations where a contraction of the drilledwell can hinder an installation of the liner later on. Furthermore,drilling with liner in depleted and unstable reservoirs minimizes therisk that the pipe or drill string will get stuck due to boreholecollapse.

Although FIG. 1 is shown and described with respect to a drillingoperation, those of skill in the art will appreciate that similarconfigurations, albeit with different components, can be used forperforming different downhole operations. For example, wireline, wiredpipe, liner drilling, reaming, coiled tubing, and/or otherconfigurations can be used as known in the art. Further, productionconfigurations can be employed for extracting and/or injecting materialsfrom/into earth formations. Thus, the present disclosure is not to belimited to drilling operations but can be employed for any appropriateor desired downhole operation(s).

Severe vibrations in drillstrings and bottomhole assemblies duringdrilling operations can be caused by cutting forces at the drill bit ormass imbalances in downhole tools such as drilling motors. Suchvibrations can result in reduced rate of penetration, reduced quality ofmeasurements made by tools of the bottomhole assembly, and can result inwear, fatigue, and/or failure of downhole components. As appreciated bythose of skill in the art, different vibrations exist, such as lateralvibrations, axial vibrations, and torsional vibrations. For example,stick/slip of the whole drilling system and high-frequency torsionaloscillations (“HFTO”) are both types of torsional vibrations. The terms“vibration,” “oscillation,” as well as “fluctuation,” are used with thesame broad meaning of repeated and/or periodic movements or periodicdeviations from a mean value, such as a mean position, a mean velocity,a mean acceleration, a mean force, and/or a mean torque. In particular,these terms are not meant to be limited to harmonic deviations, but mayinclude all kinds of deviations, such as, but not limited to periodic,harmonic, and statistical deviations. Torsional vibrations may beexcited by self-excitation mechanisms that occur due to the interactionof the drill bit or any other cutting structure such as a reamer bit andthe formation. The main differentiator between low frequency torsionaloscillations (such as stick/slip) and HFTO is the frequency and typicalmode shapes: For example, HFTO have a frequency that is typically above50 Hz compared to low frequency torsional vibrations that typically havefrequencies below 1 Hz. Moreover, the excited mode shape of lowfrequency torsional vibrations or stick/slip is typically a first modeshape of the whole drilling system whereas the mode shape of HFTO can beof higher order and are commonly localized to smaller portions of thedrilling system with comparably high amplitudes at the point ofexcitation that may be the drill bit or any other cutting structure(such as a reamer bit), or any contact between the drilling system andthe formation (e.g., by a stabilizer).

Due to the high frequency of the vibrations, HFTO correspond to highacceleration and torque values along the BHA. Those skilled in the artwill appreciate that for torsional movements, one of acceleration,force, and torque is always accompanied by the other two ofacceleration, force, and torque. In that sense, acceleration, force, andtorque are equivalent in the sense that none of these can occur withoutthe other two. The loads of high frequency vibrations can have negativeimpacts on efficiency, reliability, and/or durability of electronic andmechanical parts of the BHA. Embodiments provided herein are directed toproviding torsional vibration damping upon the downhole system tomitigate HFTO. In some embodiments of the present disclosure, thetorsional vibration damping can be activated if a threshold of ameasured property, such as a torsional vibration amplitude or frequencyis achieved within the system.

In accordance with a non-limiting embodiment provided herein, avibration damper, or in the context of this disclosure simply a damper,also known as a damping system, e.g. a torsional vibration dampingsystem, may be based on friction dampers. For example, according to someembodiments, the damper may comprise one or more damper elements thatmay be included in a damper element sub. Friction between two partswithin the damper element, such as two interacting bodies in the damperelement can dissipate energy and reduce the level of torsionaloscillations, thus mitigating the potential damage caused by highfrequency vibrations. Preferably, the energy dissipation of the damperis at least equal to the HFTO energy input caused by the bit-rockinteraction.

Friction dampers, as provided herein, can lead to a significant energydissipation and thus mitigation of torsional vibrations. When twocomponents or interacting bodies are in contact with each other and moverelative to each other, a friction force acts in the opposite directionof the velocity of the relative movement between the contacting surfacesof the components or interacting bodies. The friction force leads to adissipation of energy.

FIG. 2 is an illustrative plot 200 of a typical curve of the frictionforce or torque versus relative velocity ν (e.g., or relative rotationalspeed) between two interacting bodies. The two interacting bodies have acontact surface and a force component F_(N) perpendicular to the contactsurface engaging the two interacting bodies. Plot 200 illustrates thedependency of friction force or torque of the two interacting bodieswith a velocity-weakening behavior (e.g., frictional, the characteristicof cutting). At higher relative velocities (ν>0) between the twointeracting bodies, the friction force or torque has a distinct value,illustrated by point 202. Decreasing the relative velocity will lead toan increasing friction force or torque (also referred to asvelocity-weakening characteristic). The friction force or torque reachesits maximum when the relative velocity is zero. The maximum frictionforce is also known as static friction, sticking friction, or stiction.

Generally, friction force F_(R) depends on the normal force as describedin the equation F_(R)=μ·F_(N), with friction coefficient μ. Generally,the friction coefficient μ is a function of velocity. Herein, the normalforce can also be fluctuating corresponding to an excited vibration inthe normal direction. In the case that the relative speed between twointeracting bodies is zero (ν=0), the static friction force F_(S) isrelated to the normal force component F_(N) by the equationF_(S)=μ₀·F_(N) with the static friction coefficient μ₀. In the case thatthe relative speed between the two interacting bodies is not zero (ν≠0),the friction coefficient is known as dynamic friction coefficient μ. Ifthe relative velocity is further decreased to negative values (i.e., ifthe direction the relative movement of the two interacting bodies isswitched to the opposite), the friction force or torque switches to theopposite direction with a high absolute value corresponding to a stepfrom a positive maximum to a negative minimum at point 204 in plot 200.That is, the friction force versus velocity shows a sign change at thepoint where the velocity changes the sign and is discontinuous at point204 in plot 200. Velocity-weakening characteristic is a well-knowneffect between interacting bodies that are frictionally connected. Thevelocity-weakening characteristic of the contact force or torque isassumed to be a potential root cause for stick/slip. Velocity-weakeningcharacteristic may also be achieved by utilizing dispersive fluid with ahigher viscosity at lower relative velocities and a lower viscosity athigher relative velocities. If a dispersive fluid is forced through arelatively small channel, the same effect can be achieved in that theflow resistance is relatively high or low at low or high relativevelocities, respectively.

With reference to FIGS. 8A-8B, FIG. 8A illustrates measured torsionalacceleration of a downhole system versus time. In the 5 secondmeasurement time shown in FIG. 8A, FIG. 8A shows oscillating torsionalacceleration with a mean acceleration of approximately 0 g, overlayed byoscillating torsional accelerations with a relatively low amplitudebetween approximately 0 s and 3 s and relatively high amplitudes up to100 g between approximately 3 s and 5 s. FIG. 8B illustrates thecorresponding rotary velocity in the same time period as in FIG. 8A. Inaccordance with FIG. 8A, FIG. 8B illustrates a mean velocity ν₀(indicated by the line ν₀ in FIG. 8B) which is relatively constant atapproximately 190 rev/min. The mean velocity is overlayed by oscillatingrotary velocity variations with relatively low amplitudes betweenapproximately 0 s and 3 s and relatively high amplitudes betweenapproximately 3 s and 5 s in accordance with the relatively low and highacceleration amplitudes in FIG. 8A. Notably, the oscillating rotaryspeed does not lead to negative values of the rotary velocity, even notin the time period between approximately 3 s and 5 s when the amplitudesof the rotary speed oscillations are relatively high.

Referring again to FIG. 2 , point 202 illustrates a mean velocity of thetwo interacting bodies that is according to the mean velocity ν₀ in FIG.8B. In the schematic illustration of FIG. 2 , the data of FIG. 8Bcorresponds to a point with a velocity oscillating with relatively highfrequency due to HTFO around the mean velocity ν₀ that varies relativelyslowly with time compared to the HFTO. The point illustrating the dataof FIG. 8B therefore moves back and forth on the positive branch of thecurve in FIG. 2 without or only rarely reaching negative velocityvalues. Accordingly, the corresponding friction force or torqueoscillates around a positive mean friction force or mean friction torqueand is generally positive or only rarely reaches negative values. Asdiscussed further below, the point 202 illustrates where a positive meanvalue of the relative velocity corresponds to a static torque and thepoint 204 illustrates a favorable point for friction damping. It isnoted that friction forces or torque between the drilling system and theborehole wall will not generate additional damping of high frequencyoscillations in the system. This is because the relative velocitybetween the contact surfaces of the interacting bodies (e.g., astabilizer and the borehole wall) does not have a mean velocity that isso close to zero that the HFTO lead to a sign change of the relativevelocity of the two interacting bodies. Rather, the relative velocitybetween the two interacting bodies has a high mean value at a distancefrom zero that is large so that the HFTO do not lead to a sign change ofthe relative velocity of the two interacting bodies (e.g., illustratedby point 202 in FIG. 2 ).

As will be appreciated by those of skill in the art, the weakeningcharacteristic of the contact force or torque with respect to therelative velocity as illustrated in FIG. 2 , leads to an application ofenergy into the system for oscillating relative movements of theinteracting bodies with a mean velocity ν₀ that is high compared to thevelocity of the oscillating movement. In this context, other examples ofself-excitation mechanisms such as coupling between axial and torsionaldegree of freedom could lead to a similar characteristic.

The corresponding hysteresis is depicted in FIG. 3 and the time plot forthe friction force and velocity is shown in FIG. 4 . FIG. 3 illustrateshysteresis of a friction force F_(r), sometimes also referred to as acutting force in this context, versus displacement relative to alocation that is moving with a positive mean relative velocity withadditional small velocity fluctuations leading to additional smalldisplacement dx. Accordingly, FIG. 4 illustrates the friction force(F_(r)), relative velocity

$\left( \frac{dx}{d\;\tau} \right),$and a product of both (indicated by label 400 in FIG. 4 ) for a positivemean relative velocity with additional small velocity fluctuationsleading to additional small displacement dx. Those skilled in the art,will appreciate that the area between the friction force and thevelocity over time is equal to the dissipated energy (i.e., the areabetween the line 400 and the zero axis), which is negative in the casethat is illustrated by FIG. 3 and FIG. 4 . That is, in the caseillustrated by FIGS. 3 and 4 , energy is transferred into theoscillation from the friction via the frictional contact.

Referring again to FIG. 2 , the point 204 denotes the favorable meanvelocity for friction damping of small velocity fluctuations orvibrations in addition to the mean velocity. For small fluctuations ofthe relative movement between the two interacting bodies, thediscontinuity at point 204 in FIG. 2 with the sign change of therelative velocity of the interacting bodies also leads to an abrupt signchange of the friction force or torque. This sign change leads to ahysteresis that leads to a large amount of dissipated energy. Forexample, compare FIGS. 5 and 6 , which are similar plots to FIGS. 3 and4 , respectively, but illustrate the case of zero mean relative velocitywith additional small velocity fluctuations or vibrations. The areabelow the line 600 in FIG. 6 that corresponds to the product

$F_{r} \cdot \frac{dx}{d\;\tau}$is equal to the dissipated energy during one period and is, in thiscase, positive. That is, in the case illustrated by FIGS. 5 and 6 , theenergy is transferred from the high frequency oscillation via thefrictional contact into the friction. The effect is comparably highcompared to the case illustrated by FIGS. 3 and 4 and has the desiredsign. It is also clear from the comparison of FIGS. 2, 5, and 6 that thedissipated energy significantly depends on the difference betweenmaximum friction force and minimum friction force for ν=0 (i.e.,location 204 in FIG. 2 ). The higher the difference between maximumfriction force and minimum friction force for ν=0, the higher is thedissipated energy. While FIGS. 3-4 were generated by using velocityweakening characteristics, such as the one shown in FIG. 2 , embodimentsof the present disclosure are not limited to such type ofcharacteristics. The apparatuses and methods disclosed herein will befunctional for any type of characteristic provided that the frictionforce or torque undergoes a step with a sign change when the relativevelocity between the two interacting bodies changes its sign.

Friction dampers in accordance with some embodiments of the presentdisclosure will now be described. The friction dampers are installed onor in a drilling system, such as drilling system 10 shown in FIG. 1 ,and/or are part of drilling system 10, such as part of the bottomholeassembly 90. Friction damper elements are part of friction dampers andmay comprise two interacting bodies, such as a first element and asecond element having a frictional contact surface with the firstelement. The friction dampers of the present disclosure are arranged sothat the first element has a mean velocity that is related to the rotaryspeed of the drilling system to which it is installed. For example, thefirst element may have a similar or the same mean velocity or rotaryspeed as the drilling system, so that small fluctuating oscillationslead to a sign change or zero crossing of the relative velocity betweenthe first element and second element according to point 204 in FIG. 2 .

It is noted that friction forces or torque between the drilling systemand the borehole wall will not generate additional damping of highfrequency oscillations in the system. This is because the relativevelocity between the contact surfaces (e.g., a stabilizer and theborehole) does not have a zero mean value (e.g., point 202 in FIG. 2 ).In accordance with embodiments described herein, the static frictionbetween the first element and the second element are set to be highenough to enable the first element to accelerate the second element(during rotation) to a mean velocity ν₀ with the same value as thedrilling system. Additional high frequency oscillations, therefore,introduce slipping between the first element and the second element withpositive or negative velocities according to oscillations around aposition in FIG. 2 that is equal to or close to point 204 in FIG. 2 .Slipping occurs if the inertial force F₁ exceeds the static frictionforce, expressed as the static friction coefficient multiplied by thenormal force between the two interacting bodies: F₁>μ₀·F_(N). Inaccordance with embodiments of the present disclosure, the normal forceF_(N) (e.g. caused by the contact and surface pressure of the contactsurface between the two interacting bodies) and the static frictioncoefficient μ₀ are adjusted to achieve an optimal energy dissipation andan optimal amplitude. Further, the moment of inertia (torsional), thecontact and surface pressure of the contacting surfaces, and theplacement of the damper or contact surface with respect to the distancefrom bit may be optimized.

For example, turning to FIG. 7 , a schematic illustration of a dampingsystem 700 in accordance with an embodiment of the present disclosure isshown. The damping system 700 is part of a downhole system 702, such asa bottomhole assembly and/or a drilling assembly. The downhole system702 includes a string 704 that is rotated to enable a drilling operationof the downhole system 702 to form a borehole 706 within a formation708. As discussed above, the borehole 706 is typically filled withdrilling fluid, such as drilling mud. The damping system 700 includes afirst element 710 that is operatively coupled, e.g. fixedly connected oran integral part of the downhole system 702, so as to ensure that thefirst element 710 rotates with a mean velocity that is related to, e.g.similar to or same as the mean velocity of the downhole system 702. Thefirst element 710 is in frictional contact with a second element 712.The second element 712 is at least partially movably mounted on thedownhole system 702, with a contact surface 714 located between thefirst element 710 and the second element 712.

In the case of frictional forces, the difference between the minimum andmaximum friction force is positively dependent on the normal force andthe static friction coefficient. The dissipated energy increases withfriction force and the harmonic displacement, but, only in a slip phase,energy is dissipated. In a sticking phase, the relative displacementbetween the friction interfaces and the dissipated energy is zero. Theupper amplitude limit of the sticking phase increases linearly with thenormal force and the friction coefficient in the contact interface. Thereason is that the reactive force in the contact interface, J{umlautover (x)}≥M_(H)=F_(N)μ_(H)r, that can be caused by the moment of inertiaJ of one of the contacting bodies if it is accelerated with z has to behigher than the torque M_(H)=F_(N)μ_(H)r that defines the limit betweensticking and slipping. As used herein, F_(N) is the normal force andμ_(H) is the effective friction coefficient and r is the effective ormean radius of the friction contact area. For complex frictionalcontacts parts of the interacting bodies, sticking or slipping can occurat the same time. Herein the contact pressure can be optimized toachieve an optimal damping and amplitude.

Similar mechanisms apply if the contact force is caused by adisplacement and spring element. The acceleration {umlaut over (x)} ofthe contact area can be due to an excitation of a mode and is dependentupon the corresponding mode shape, as further discussed below withrespect to FIG. 9B. In case of an attached inertial mass (or simplyinertia or mass within the context of this disclosure) with moment ofinertia J the acceleration {umlaut over (x)} is equal to theacceleration of the excited mode and corresponding mode shape at theattachment position as long as the contact interface is sticking.

The normal force and friction force have to be adjusted to guarantee aslipping phase in an adequate or tolerated amplitude range. A toleratedamplitude range can be defined by an amplitude that is between zero andthe limits of loads that are, for example, given by designspecifications of tools and components. A limit could also be given by apercentage of the expected amplitude without the damper. The dissipatedenergy that can be compared to the energy input, e.g., by a forced orself-excitation, is one measure to judge the efficiency of a damper.Another measure is the provided equivalent damping of the system that isproportional to the ratio of the dissipated energy in one period of aharmonic vibration to the potential energy during one period ofvibration in the system. This measure is especially effective in case ofself-excited systems. In the case of self-excited systems, theexcitation can be approximated by a negative damping coefficient andboth the equivalent damping and the negative damping can be directlycompared. The damping force that is provided by the damper is nonlinearand strongly amplitude dependent.

As shown in FIG. 20 , the damping is zero in the sticking phase (leftend of plot of FIG. 20 ) where the relative movement between theinteracting bodies is zero. If, as described above, the limit betweenthe sticking and slipping phase is exceeded by the force that istransferred through the contact interface, a relative sliding motion isoccurring that causes the energy dissipation. The damping ratio providedby the friction damping is then increasing to a maximum and afterwardsdeclining to a minimum. The amplitude that will be occurring isdependent upon the excitation that could be described by the negativedamping term. Herein, the maximum of the damping provided, as depictedin FIG. 20 , has to be higher than the negative damping from theself-excitation mechanism. The amplitude that is occurring in aso-called limit cycle can be determined by the intersection of thenegative damping ratio and the equivalent damping ratio that is providedby the friction damper.

The curve is dependent on different parameters. It is beneficial to havea high normal force but a sliding phase with a minimum amplitude. In thecase of the inertial mass, this can be achieved by a high mass or byplacing the contact interface at a point of high acceleration withrespect to the excited mode shape. In the case of contacting interfaces,a high relative displacement in comparison to the amplitude of the modeshape at the contact point, e.g., along the axial axis of the BHA, isbeneficial. Therefore, an optimal placement of the damper according to ahigh amplitude or relative amplitude is important. This can be achievedby using simulation results, as discussed below. The normal force andthe friction coefficient can be used to shift the curve to lower orhigher amplitudes but does not have a high influence on the dampingmaximum. If more than one friction damper is implemented, this wouldlead to a superposition of similar curves shown in FIG. 20 . If thenormal force and friction coefficients are adjusted to achieve themaximum at the same amplitude, this is beneficial for the overalldamping that is achieved. Further, slightly shifted damping curves wouldlead to a resulting curve that could be broader with respect to theamplitude that could be beneficial to account for impacts that couldshift the amplitude to the right of the maximum. In this case, theamplitude would increase to a very high value in case of self-excitedsystems as indicated by the negative damping. In this case, theamplitude needs to be shifted again to the left side of the maximum,e.g., by going off bottom or reducing the rotary speed of the system tolower levels. The amplitude in this context approximately linearlyscales by the mean rotary speed as indicated and discussed with respectto FIG. 8B, below.

Referring again to FIG. 7 , the string 704, and thus the downhole system702, rotates with a rotary speed dφ/dτ, that may be measured inrevolutions per minute (RPM). The second element 712 is mounted onto thefirst element 710. A normal force F_(N) between the first element 710and the second element 712 can be selected or adjusted throughapplication and use of an adjusting element 716. The adjusting element716 may be adjustable, for example via a thread, an actuator, apiezoelectric actuator, a hydraulic actuator, and/or a spring element,to apply force that has a component in the direction perpendicular tothe contact surface 714 between the first element 710 and the secondelement 712. For example, as shown in FIG. 7 , the adjusting element 716may apply a force in axial direction of downhole system 702, thattranslates into a force component F_(N) that is perpendicular to thecontact surface 714 of first element 710 and second element 712 due tothe non-zero angle between the axis of the downhole system 702 and thecontact surface 714 of first element 710 and second element 712. In someconfigurations, an angle between the system 712 and the inertial masselement is selected or defined to allow a sliding motion and avoidself-locking.

The second element 712 has a moment of inertia J. When HFTO occursduring operation of the downhole system 702, both the downhole system702 and the second element 712 are accelerated according to a mode shape(e.g., defines the amplitude distribution along the dimensions of thedrilling system, drill string, and/or BHA) and the amplitude of the mode(e.g., scales the amplitude of the mode shape). Exemplary results ofsuch operation are shown in FIGS. 8A and 8B. FIG. 8A is a plot oftangential (i.e., circumferential) acceleration measured at a drill bitand FIG. 8B is a corresponding rotary speed.

Due to the tangential acceleration and the inertia of the second element712, relative inertial forces occur between the second element 712 andthe first element 710. If these inertial forces exceed a thresholdbetween sticking and slipping, i.e., if these inertial forces exceedstatic friction force between the first element 710 and the secondelement 710, a relative movement between the elements 710, 712 willoccur that leads to energy dissipation. In such arrangements, theaccelerations, the static and/or dynamic friction coefficient, and thenormal force determine the amount of dissipated energy. For example, themoment of inertia J of the second element 712 determines the relativeforce that has to be transferred between the first element 710 and thesecond element 712. High accelerations and moments of inertia increasethe tendency for slipping at the contact surface 714 and thus lead to ahigher energy dissipation and equivalent damping ratio provided by thedamper.

Due to the energy dissipation that is caused by frictional movementbetween the first element 710 and the second element 712, heat and wearwill be generated on the first element 710 and/or the second element712. To keep the wear below an acceptable level, materials can be usedfor the first and/or second elements 710, 712 that can withstand thewear. For example, diamonds or polycrystalline diamond compacts can beused for, at least, a portion of the first and/or second elements 710,712. Alternatively, or in addition, coatings may help to reduce the weardue to the friction between the first and second elements 710, 712. Theheat can lead to high temperatures and may impact reliability ordurability of the first element 710, the second element 712, and/orother parts of the downhole system 702. The first element 710 and/or thesecond element 712 may be made of a material with high thermalconductivity or high heat capacity and/or may be in contact with amaterial with high thermal conductivity or heat capacity.

Such materials with high thermal conductivity include, but are notlimited to, metals or compounds including metal, such as copper, silver,gold, aluminum, molybdenum, tungsten or thermal grease comprising fat,grease, oil, epoxies, silicones, urethanes, and acrylates, andoptionally fillers such as diamond, metal, or chemical compoundsincluding metal (e.g., silver, aluminum in aluminum nitride, boron inboron nitride, zinc in zinc oxide), or silicon or chemical compoundsincluding silicon (e.g., silicon carbide). In addition or alternatively,one or both of the first element 710 and the second element 712 may bein contact with a fluid, such as the drilling fluid, that is configuredto remove heat from the first element 710 and/or the second element 712in order to cool the respective element 710, 712. Further, an amplitudelimiting element (not shown), such as a key, a recess, or a springelement may be employed and configured to limit the energy dissipationto an acceptable limit that reduces the wear.

When arranging the damping system 700, a high normal force and/or staticor dynamic friction coefficient will prevent a relative slipping motionbetween the first element 710 and the second element 712, and in suchsituations, no energy will be dissipated. In contrast, a low normalforce and/or static or dynamic friction coefficient can lead to a lowfriction force and slipping will occur but the dissipated energy is low.In addition, low normal force and/or static or dynamic frictioncoefficient may lead to the case that the friction at the outer surfaceof the second element 712, e.g., between the second element 712 and theformation 708, is higher than the friction between first element 710 andsecond element 712, thus leading to the situation that the relativevelocity between first element 710 and second element 712 is not equalto or close to zero but is in the range of the mean velocity betweendownhole system 702 and formation 708. As such, the normal force and thestatic or dynamic friction coefficient and the placement of the damperelement with respect to the exited mode and mode shape may be adjusted(e.g., by using the adjusting element 716) to achieve an optimized valuefor energy dissipation.

This can be done by adjusting the normal force F_(N), the staticfriction coefficient μ₀, the dynamic friction coefficient μ, theplacement of the damper element with respect to the excited mode shape,or combinations thereof. The normal force F_(N) can be adjusted bypositioning the adjusting element 716 and/or by actuators that generatea force on one of the first and second elements with a componentperpendicular to the contact surface of first and second element, byadjusting the pressure regime around first and second element, or byincreasing or decreasing an area where a pressure is acting on. Forexample, by increasing the outer pressure that acts on the secondelement, such as the mud pressure, the normal force F_(N) will beincreased as well. Adjusting the pressure of the mud downhole may beachieved by adjusting the mud pumps (e.g., mud pumps 34 shown in FIG. 1) on surface or other equipment on surface or downhole that influencesthe mud pressure, such as bypasses, valves, desurgers. The normal forcecan be adjusted to be harmonic with the same frequency as the naturalfrequency of the excited mode shape and thus have low normal forcevalues for low acceleration of the inertial mass and high normal forcevalues for low accelerations of the inertial mass and therefor allowsliding motion for low acceleration values.

The normal force F_(N) may also be adjusted by a biasing element (notshown), such as a spring element, that applies force on the secondelement 712, e.g. a force in an axial direction away from or toward thefirst element 710. Adjusting the normal force F_(N) may also be done ina controlled way based on an input received from a sensor. For example,a suitable sensor (not shown) may provide one or more parameter valuesto a controller (not shown), the parameter value(s) being related to therelative movement of the first element 710 and the second element 712 orthe temperature of one or both of the first element 710 and the secondelement 712. Based on the parameter value(s), the controller may provideinstruction to increase or decrease the normal force F_(N). For example,if the temperature of one or both of the first element 710 and thesecond element 712 exceeds a threshold temperature, the controller mayprovide instruction to decrease the normal force F_(N) to prevent damageto one or both of the first element 710 and the second element 712 dueto high temperatures. Similarly, for example, if a distance, velocity,or acceleration of the second element 712 relative to the first element710 exceeds a threshold, the controller may provide instructions toincrease or decrease the normal force F_(N) to ensure optimal energydissipation. By monitoring the parameter value, the normal force F_(N)may be controlled to achieve desired results over a time period. Forinstance, the normal force F_(N) may be controlled to provide optimalenergy dissipation while keeping the temperature of one or both of thefirst element 710 and the second element 712 below a threshold for adrilling run or a portion thereof.

Additionally, the static or dynamic friction coefficient can be adjustedby utilizing different materials, for example, without limitation,material with different stiffness, different roughness, and/or differentlubrication. For example, a surface with higher roughness oftenincreases the friction coefficient. Thus, the friction coefficient canbe adjusted by choosing a material with an appropriate frictioncoefficient for at least one of the first and the second element or apart of at least one of the first and second element. The material offirst and/or second element may also have an effect on the wear of thefirst and second element. To keep the wear low of the first and secondelement it is beneficial to choose a material that can withstand thefriction that is created between the first and second elements. Theinertia, the friction coefficient, and the expected accelerationamplitudes (e.g., as a function of mode shape and eigenfrequency) of thesecond element 712 are parameters that determine the dissipated energyand also need to be optimized. The critical mode shapes and accelerationamplitudes can be determined from measurements or calculations or basedon other known methods as will be appreciated by those of skill in theart. Examples are a finite element analysis or the transfer matrixmethod or finite differences method and based on this a modal analysisor analytical models. The placement of the friction damper is optimalwhere a high relative displacement or acceleration is expected.

Turning now to FIGS. 9A and 9B, an example of a downhole system 900 andcorresponding modes are shown. FIG. 9A is a schematic plot of a downholesystem illustrating a shape of a downhole system as a function ofdistance-from-bit, and FIG. 9B illustrates example corresponding modeshapes of torsional oscillations that may be excited during operation ofthe downhole system of FIG. 9A. The illustrations of FIGS. 9A and 9Bdemonstrate the potential location and placement of one or more elementsof a damping system onto the downhole system 900.

As illustratively shown in FIG. 9A, the downhole system 900 has variouscomponents with different diameters (along with differing masses,densities, configurations, etc.) and thus during rotation of thedownhole system 900, different components may cause various modes to begenerated. The illustrative modes indicate where the highest amplitudeswill exist that may require damping by application of a damping system.For example, as shown in FIG. 9B, the mode shape 902 of a firsttorsional oscillation, the mode shape 904 of a second torsionaloscillation, and the mode shape 906 of a third torsional oscillation ofthe downhole system 900 are shown. Based on the knowledge of mode shapes902, 904, 906, the position of the first elements of damping system canbe optimized. Where an amplitude of a mode shape 902, 904, 906 ismaximum (peaks), damping may be required and/or achieved. Accordingly,illustratively shown are two potential locations for attachment orinstallation of a damping system of the present disclosure.

For example, a first damping location 908 is close to the drill bit ofdownhole system 900 and mainly damps the first and third torsionaloscillations (corresponding to mode shapes 902, 906) and provides somedamping with respect to the second torsional oscillation (correspondingto mode shape 904). That is, the first damping location 908 to beapproximately at a peak of the third torsional oscillation(corresponding to mode shape 906), close to peak of the first torsionaloscillation mode shape 902, and about half-way to peak with respect tothe second torsional oscillation mode shape 904.

A second damping location 910 is arranged to again mainly providedamping of the third torsional oscillation mode shape 906 and providesome damping with respect to the first torsional oscillation mode shape902. However, in the second damping location 910, no damping of thesecond torsional oscillation mode shape 904 will occur because thesecond torsional oscillation mode shape 904 is nearly zero at the seconddamping location 910.

Although only two locations are shown in FIGS. 9A and 9B for placementof damping systems of the present disclosure, embodiments are not to beso limited. For example, any number and any placement of damping systemsmay be installed along a downhole system to provide torsional vibrationdamping upon the downhole system. An example of a preferred installationlocation for a damper is where one or more of the expected mode shapesshow high amplitudes.

Due to the high amplitudes at the drill bit, for example, one goodlocation of a damper is close to or even within the drill bit. Further,the first and second elements are not limited to a single body but cantake any number of various configurations to achieve desired damping.That is, multiple body (multi-body) first or second elements (e.g.,friction damper) with each body having the same or different normalforces, friction coefficients, and moments of inertia can be employed.Such multiple-body element arrangements can be used, for example, if itis uncertain which mode shape and corresponding acceleration is expectedat a given position along a downhole system.

For example, two or more element bodies that can achieve differentrelative slipping motion between each other to dissipate energy may beused. The multiple bodies of the first element can be selected andassembled with different static or dynamic friction coefficients, anglesbetween the contact surfaces, and/or may have other mechanisms toinfluence the amount of friction and/or the transition between stickingand slipping. Several amplitude levels, excited mode shapes, and/ornatural frequencies can be damped with such configurations.

For example, turning to FIG. 10 , a schematic illustration of a dampingsystem 1000 in accordance with an embodiment of the present disclosureis shown. The damping system 1000 can operate similar to that shown anddescribed above with respect to FIG. 7 . The damping system 1000includes first element 1010 and second elements 1012. However, in thisembodiment, the second element 1012 that is mounted to the first element1010 of a downhole system 1002 is formed from a first body 1018 and asecond body 1020. The first body 1018 has a first contact surface 1022between the first body 1018 and the first element 1010 and the secondbody 1020 has a second contact surface 1024 between the second body 1020and the first element 1010. As shown, the first body 1018 is separatedfrom the second body 1020 by a gap 1026. The gap 1026 is provided toprevent interaction between the first body 1018 and the second body 1020such that they can operate (e.g., move) independent of each other or donot directly interact with each other. In this embodiment, the firstbody 1018 has a first static or dynamic friction coefficient pi and afirst force F_(N1) that is normal to the first contact surface 1022,whereas the second body 1020 has a second static or dynamic frictioncoefficient μ₂ and a second force F_(N2) that is normal to the secondcontact surface 1024. Further, the first body 1018 can have a firstmoment of inertia J₁ and the second body 1020 can have a second momentof inertia J₂. In some embodiments, at least one of the first static ordynamic friction coefficient μ₁, the first normal force F_(N1), and thefirst moment of inertia J₁ are selected to be different than the secondstatic or dynamic friction coefficient μ₂, the second normal forceF_(N2), and the second moment of inertia J₁, respectively. Thus, thedamping system 1000 can be configured to account for multiple differentmode shapes at a substantially single location along the downhole system1002.

Turning now to FIG. 11 , a schematic illustration of a damping system1100 in accordance with an embodiment of the present disclosure isshown. The damping system 1100 can operate similar to that shown anddescribed above. However, in this embodiment, a second element 1112 thatis mounted to a first element 1110 of a downhole system 1102 is formedfrom a first body 1118, a second body 1120, and a third body 1128. Thefirst body 1118 has a first contact surface 1122 between the first body1118 and the first element 1110, the second body 1120 has a secondcontact surface 1124 between the second body 1120 and the first element1110, and the third body 1128 has a third contact surface 1130 betweenthe third body 1128 and the first element 1110. As shown, the third body1128 is located between the first body 1118 and the second body 1020. Inthis embodiment, the three bodies 1118, 1120, 1128 are in contact witheach other and thus can have normal forces and static or dynamicfriction coefficients therebetween.

The contact between the three bodies 1118, 1120, 1128 may beestablished, maintained, or supported by elastic connection elementssuch as spring elements between two or more of the bodies 1118, 1120,1128. In addition, or alternatively, the first body 1118 may have afirst static or dynamic friction coefficient μ₁ and a first force F_(N1)at the first contact surface 1122, the second body 1120 may have asecond static or dynamic friction coefficient μ₂ and a second forceF_(N2) at the second contact surface 1124, and the third body 1128 mayhave a third static or dynamic friction coefficient μ₃ and a third forceF_(N3) at the third contact surface 1130.

In addition, or alternatively, the first body 1118 and the third body1128 may have a fourth force F_(N13) and a fourth static or dynamicfriction coefficient μ₁₃ between each other at a contact surface betweenthe first body 1118 and the third body 1128. Similarly, the third body1128 and the second body 1120 may have a fifth force F_(N32) and a fifthstatic or dynamic friction coefficient μ₃₂ between each other at acontact surface between the third body 1128 and the second body 1120.

Further, the first body 1118 can have a first moment of inertia J₁, thesecond body 1120 can have a second moment of inertia J₂, and the thirdbody 1128 can have a third moment of inertia J₃. In some embodiments,the static or dynamic friction coefficients μ₁, μ₂, μ₃, μ₁₃, μ₃₂, theforces F_(N1), F_(N2), F_(N3), F₁₃, F₃₂, and the moment of inertia J₁,J₂, J₃ can be selected to be different than each other so that theproduct μ_(i)·F_(i) (with i=1, 2, 3, 13, 32) are different for at leasta subrange of the relative velocities of first element 1110, first body1118, second body 1120, and third body 1128. Moreover, the static ordynamic friction coefficients and normal forces between adjacent bodiescan be selected to achieve different damping effects.

Although shown and described with respect to a limited number ofembodiments and specific shapes, relative sizes, and numbers ofelements, those of skill in the art will appreciate that the dampingsystems of the present disclosure can take any configuration. Forexample, the shapes, sizes, geometries, radial placements, contactsurfaces, number of bodies, etc. can be selected to achieve a desireddamping effect. While in the arrangement that is shown in FIG. 11 , thefirst body 1118 and the second body 1120 are coupled to each other bythe frictional contact to the third body 1128, such arrangement anddescription is not to be limiting. The coupling between the first body1118 and the second body 1120 may also be created by a hydraulic,electric, or mechanical coupling means or mechanism. For example, amechanical coupling means between the first body 1118 and the secondbody 1120 may be created by a rigid or elastic connection of first body1118 and the second body 1120.

Turning now to FIG. 12 , a schematic illustration of a damping system1200 in accordance with an embodiment of the present disclosure isshown. The damping system 1200 can operate similar to that shown anddescribed above. However, in this embodiment, a second element 1212 ofthe damping system 1200 is partially fixedly attached to or connected toa first element 1210. For example, as shown in this embodiment, thesecond element 1212 has a fixed portion 1232 (or end) and a movableportion 1234 (or end). The fixed portion 1232 is fixed to the firstelement 1210 along a fixed connection 1236 and the movable portion 1234is in frictional contact with the first element 1210 across the contactsurface 1214 (similar to the first element 1010 in frictional contactwith the second element 1012 described with respect to FIG. 10 ).

The movable portion 1234 can have any desired length that may be relatedto the mode shapes as shown in FIG. 9B. For example, in someembodiments, the movable portion may be longer than a tenth of thedistance between the maximum and the minimum of any of the mode shapesthat may have been calculated for a particular drilling assembly. Inanother example, in some embodiments, the movable portion may be longerthan a quarter of the distance between the maximum and the minimum ofany of the mode shapes that may have been calculated for a particulardrilling assembly. In another example, in some embodiments, the movableportion may be longer than a half of the distance between the maximumand the minimum of any of the mode shapes that may have been calculatedfor a particular drilling assembly. In another example, in someembodiments, the movable portion may be longer than the distance betweenthe maximum and the minimum of any of the mode shapes that may have beencalculated for a particular drilling assembly.

As such, even though it may not be known where the exact location ofmode maxima or minima is during a downhole deployment, it is assuredthat the second element 1212 is in frictional contact with the firstelement 1210 at a position of maximum amplitude to achieve optimizeddamping. Although shown with a specific arrangement, those of skill inthe art will appreciate that other arrangements of partially fixed firstelements are possible without departing from the scope of the presentdisclosure. For example, in one non-limiting embodiment, the fixedportion can be in a more central part of the first element such that thefirst element has two movable portions (e.g., at opposite ends of thefirst element). As can be seen in FIG. 12 , the movable portion 1234 ofthe second element 1212 is rather elongated and may cover a portion ofthe mode shapes (such as mode shapes 902, 904, 906 in FIG. 9B) thatcorrespond to the length of the movable portion 1234 of the secondelement 1212. An elongated second element 1212 in frictional contactwith the first element 1210 may have advantages compared to shortersecond elements because shorter second elements may be located in anundesired portion of the mode shapes such as in a damping location 910where the second mode shape 904 is small or even zero as explained abovewith respect to FIG. 9B. Utilizing an elongated second element 1212 mayensure that at least a portion of the second element is at a distancefrom locations where one or more of the mode shapes are zero or at leastclose to zero. FIGS. 13-19 and 21-22 show more varieties of elongatedsecond elements in frictional contact with first elements. In someembodiments, the elongated second elements may be elastic so that themovable portion 1234 is able move relative to the first element 1210while the fixed portion 1232 is stationary relative to first element1210. In some embodiments, the second element 1212 may have multiplecontact points at multiple locations of the first element 1210.

In the above described embodiments, and in damping systems in accordancewith the present disclosure, the first elements are temporarily fixed tothe second elements due to a friction contact. However, as vibrations ofthe downhole systems increase, and exceed a threshold, e.g., when aforce of inertia exceeds the static friction force, the first elements(or portions thereof) move relative to the second elements, thusproviding the damping. That is, when HFTO increase above predeterminedthresholds (e.g., thresholds of amplitude, distance, velocity, and/oracceleration) within the downhole systems, the damping systems willautomatically operate, and thus embodiments provided herein includepassive damping systems. For example, embodiments include passivedamping systems automatically operating without utilizing additionalenergy and therefore do not utilize an additional energy source.

Turning now to FIG. 13 , a schematic illustration of a damping system1300 in accordance with an embodiment of the present disclosure isshown. In this embodiment, the damping system 1300 includes one or moreelongated first elements 1310 a, 1310 b, 1310 c, 1310 d, 1310 e, 1310 f,each of which is arranged within and in contact with a second element1312. Each of the first elements 1310 a, 1310 b, 1310 c, 1310 d, 1310 e,1310 f may have a length in an axial tool direction (e.g., in adirection perpendicular to the cross-section that is shown in FIG. 13 )and optionally a fixed point where the respective first elements 1310 a,1310 b, 1310 c, 1310 d, 1310 e, 1310 f are fixed to the second element1312. For example, the first elements 1310 a, 1310 b, 1310 c, 1310 d,1310 e, 1310 f can be fixed at respective upper ends, middle portions,lower ends, or multiple points of fixation for the different firstelements 1310 a, 1310 b, 1310 c, 1310 d, 1310 e, 1310 f, or multiplepoints for a given single first element 1310 a, 1310 b, 1310 c, 1310 d,1310 e, 1310 f. Further, as shown in FIG. 13 , the first elements 1310a, 1310 b, 1310 c, 1310 d, 1310 e, 1310 f can be optionally biased orengaged to the second element 1312 by a biasing element 1338 (e.g., by abiasing spring element or a biasing actuator applying a force with acomponent toward the second element 1312). Each of the first elements1310 a, 1310 b, 1310 c, 1310 d, 1310 e, 1310 f can be arranged andselected to have the same or different normal forces, static or dynamicfriction coefficients, and moments of inertia, thus enabling variousdamping configurations.

In some embodiments, the first elements may be substantially uniform inmaterial, shape, and/or geometry along a length thereof. In otherembodiments, the first elements may vary in shape and geometry along alength thereof. For example, with reference to FIG. 14 , a schematicillustration of a damping system 1400 in accordance with an embodimentof the present disclosure is shown. In this embodiment, a first element1410 is arranged relative to a second element 1412, and the firstelement 1410 has a tapering and/or spiral arrangement relative to thesecond element 1412. Accordingly, in some embodiments, a portion of thefirst or second element can change geometry or shape along a lengththereof, relative to the second element, and such changes can also occurin a circumferential span about or relative to the second element and/orwith respect to a tool body or downhole system.

Turning now to FIG. 15 , a schematic illustration of another dampingsystem 1500 in accordance with an embodiment of the present disclosureis shown. In the damping system 1500, a first element 1510 is a toothed(threaded) body that is fit within a threaded second element 1512. Thecontact between the teeth (threads) of the first element 1510 and thethreads of the second element 1512 can provide the frictional contactbetween the two elements 1510, 1512 to enable damping as describedherein. Due to the slanted surfaces of the first element 1510, the firstelement 1510 will start to move under both axial and/or torsionalvibrations. Further, movement of first element 1510 in an axial orcircumferential direction will also create movement in thecircumferential or axial direction, respectively, in this configuration.Therefore, with the arrangement shown in FIG. 15 , axial vibrations canbe utilized to mitigate or damp torsional vibrations as well astorsional vibrations can be utilized to mitigate or damp axialvibrations.

The locations where the axial and torsional vibrations occur may bedifferent. For example, while the axial vibrations may be homogeneouslydistributed along the drilling assembly, the torsional vibrations mayfollow a mode shape pattern as discussed above with respect FIGS. 9A-9B.Thus, irrespective of where the vibrations occur, the configurationshown in FIG. 15 may be utilized to damp torsional vibrations with themovement of the first element 1510 relative to the second element 1512caused by the axial vibrations and vice versa. As shown, an optionaltightening element 1540 (e.g., a bolt) can be used to adjust the contactpressure or normal force between the two elements 1510, 1512, and thusadjust the frictional force and/or other damping characteristics of thedamping system 1500.

Turning now to FIG. 16 , a schematic illustration of a damping system1600 in accordance with another embodiment of the present disclosure isshown. The damping system 1600 that includes a first element 1610 thatis a stiff rod that is at one end fixed within a second element 1612. Inthis embodiment, a rod end 1610 a is arranged to frictionally contact asecond element stop 1612 a to thus provide damping as described inaccordance with embodiments of the present disclosure. The normal forcebetween the rod end 1610 a and the second element stop 1612 a may beadjustable, for example, by a threaded connection between the rod end1610 a and the first element 1610. Further, the stiffness of the rodcould be selected to optimize the damping or influence the mode shape ina beneficial way to provide a larger relative displacement. For example,selecting a rod with a lower stiffness would lead to higher amplitudesof the torsional oscillations of the first element 1610 and a higherenergy dissipation.

Turning now to FIG. 17 , a schematic illustration of a damping system1700 in accordance with another embodiment of the present disclosure isshown. The damping system 1700 that includes a first element 1710 thatis frictionally attached or connected to a second element 1712 that isarranged as a stiff rod and that is fixedly connected (e.g., by welding,screwing, brazing, adhesion, etc.) to an outer tubular 1714, such as adrill collar, at a fixed connection 1716. In one aspect, the rod may bea tubular that includes electronic components, power supplies, storagemedia, batteries, microcontrollers, actuators, sensors, etc. that areprone to wear due to HFTO. That is, in one aspect, the second element1712 may be a probe, such as a probe to measure directional information,including one or more of a gravimeter, a gyroscope, and a magnetometer.In this embodiment, the first element 1710 is arranged to frictionallycontact, move, or oscillate relative to and along the fixed rodstructure of the second element 1712 to thus provide damping asdescribed in accordance with embodiments of the present disclosure.While the first element 1710 is shown in FIG. 17 to be relatively smallcompared to the damping system 1700, it is not meant to be limited inthat respect. Thus, the first element can 1710 can be of any size andcan have the same outer diameter as the damping system 1700. Further,the location of the first element 1710 may be adjustable in order tomove the first element 1710 closer to a mode shape maximum to optimizedamping mitigation.

Turning now to FIG. 18 , a schematic illustration of a damping system1800 in accordance with another embodiment of the present disclosure isshown. The damping system 1800 that includes a first element 1810 thatis frictionally movable along a second element 1812. In this embodiment,the first element 1810 is arranged with an elastic spring element 1842,such as a helical spring or other element or means, to engage the firstelement 1810 with the second element 1812, and to thus provide arestoring force when the first element 1810 has moved and is deflectedrelative to the second element. The restoring force is directed toreduce the deflection of the first element 1810 relative to the secondelement 1812. In such embodiments, the elastic spring element 1842 canbe arranged or tuned to resonance and/or to a critical frequency (e.g.,lowest critical frequency) of the elastic spring element 1842 or theoscillation system comprising the first element 1810 and the elasticspring element 1842.

Turning now to FIG. 19 , a schematic illustration of a damping system1900 in accordance with another embodiment of the present disclosure isshown. The damping system 1900 that includes a first element 1910 thatis frictionally movable about a second element 1912. In this embodiment,the first element 1910 is arranged with a first end 1910 a having afirst contact (e.g., first end normal force F_(Ni), first end static ordynamic friction coefficient μ_(i), and first end moment of inertia J₁)and a second contact at a second end 1910 b (e.g., second end normalforce F_(Ni), second end static or dynamic friction coefficient μ_(i),and second end moment of inertia J_(i)). In some such embodiments, thetype of interaction between the respective first end 1910 a or secondend 1910 b and the second element 1912 may have different physicalcharacteristics. For example, one or both of the first end 1910 a andthe second end 1910 b may have a sticking contact/engagement and one orboth may have a sliding contact/engagement. Thearrangements/configurations of the first and second ends 1910 a, 1910 bcan be set to provide damping as described in accordance withembodiments of the present disclosure.

Advantageously, embodiments provided herein are directed to systems formitigating high-frequency torsional oscillations (HFTO) of downholesystems by application of damping systems that are installed on arotating string (e.g., drill string). The first elements of the dampingsystems are, at least partially, frictionally connected to movecircumferentially relative to an axis of the string (e.g., frictionallyconnected to rotate about the axis of the string). In some embodiments,the second elements can be part of a drilling system or bottomholeassembly and does not need to be a separately installed component orweight. The second element, or a part thereof, is connected to thedownhole system in a manner that relative movement between the firstelement and the second element has a relative velocity of zero or closeto zero (i.e., no or slow relative movement) if no HFTO exists. However,when HFTO occurs above a distinct acceleration value, the relativemovement between the first element and the second element is possibleand alternating plus and minus relative velocities are achieved. In someembodiments, the second element can be a mass or weight that isconnected to the downhole system. In other embodiments, the secondelement can be part of the downhole system (e.g., part of a drillingsystem or BHA) with friction between the first element and the secondelement, such as the rest of the downhole system providing thefunctionality described herein.

As described above, the second elements of the damping systems areselected or configured such that when there is no vibration (i.e., HFTO)in the string, the second element will be frictionally connected to thefirst element by the static friction force. However, when there isvibration (HFTO), the second elements become moving with respect to thefirst element and the frictional contact between the first and thesecond element is reduced as described above with respect to FIG. 2 ,such that the second element can rotate (move) relative to the firstelement (or vice versa). When moving, the first and second elementsenable energy dissipation, thus mitigating HFTO. The damping systems,and particularly the first elements thereof, are positioned, weighted,forced, and sized to enable damping at one or more specific orpredefined vibration modes/frequencies. As described herein, the firstelements are fixedly connected when no HFTO vibration is present but arethen able to move when certain accelerations (e.g., according to HFTOmodes) are present, thus enabling damping of HFTO through a zerocrossing of a relative velocity (e.g., switching between positive andnegative relative rotational velocities).

In the various configurations discussed above, sensors can be used toestimate and/or monitor the efficiency and the dissipated energy of adamper. The measurement of displacement, velocity, and/or accelerationnear the contact point or surface of the two interacting bodies, forexample in combination with force or torque sensors, can be used toestimate the relative movement and calculate the dissipated energy. Theforce may also be known without a measurement, for example, when the twointeracting bodies are engaged by a biasing element, such as a springelement or an actuator. The dissipated energy could also be derived fromtemperature measurements. Such measurement values may be transmitted toa controller or human operator which may enable adjustment of parameterssuch as the normal force and/or the static or dynamic frictioncoefficient(s) to achieve a higher dissipated energy. For example,measured and/or calculated values of displacement, velocity,acceleration, force, and/or temperature may be sent to a controller,such as a micro controller, that has a set of instructions stored to astorage medium, based on which it adjusts and/or controls at least oneof the force that engages the two interacting bodies, and/or the staticor dynamic friction coefficients. Preferably, the adjusting and/or thecontrolling is done while the drilling process is ongoing to achieveoptimum HFTO damping results.

While embodiments described herein have been described with reference tospecific figures, it will be understood that various changes may bemade, and equivalents may be substituted for elements thereof withoutdeparting from the scope of the present disclosure. In addition, manymodifications will be appreciated to adapt a particular instrument,situation, or material to the teachings of the present disclosurewithout departing from the scope thereof. Therefore, it is intended thatthe disclosure is not limited to the particular embodiments disclosed,but that the present disclosure will include all embodiments fallingwithin the scope of the appended claims or the following description ofpossible embodiments.

Severe vibrations in drillstrings and bottomhole assemblies can becaused by cutting forces at the drill bit or mass imbalances in downholetools such as drilling motors. Negative effects are among others reducedrate of penetration, reduced quality of measurements and downholefailures.

Different sorts of torsional vibrations exist. In the literature thetorsional vibrations are mainly differentiated into stick/slip of thewhole drilling system and high-frequency torsional oscillations (HFTO).Both are mainly excited by self-excitation mechanisms that occur due tothe interaction of the drill bit and the formation. The maindifferentiator between stick/slip and HFTO is the frequency and thetypical mode shape: In case of HFTO the frequency is above 50 Hzcompared to below 1 Hz in case of stick/slip. Further the excited modeshape of stick/slip is the first mode shape of the whole drilling systemwhereas the mode shape of HFTOs are commonly localized to a smallportion of the drilling system and have comparably high amplitudes atthe drill bit.

Due to the high frequency HFTO corresponds to high acceleration andtorque values along the BHA and can have damaging effects on electronicsand mechanical parts. Based on the theory of self-excitation increaseddamping can mitigate HFTOs if a certain limit of the damping value isreached (since self-excitation is an instability and can be interpretedas a negative damping of the associated mode).

One damping concept is based on friction. Friction between two parts inthe BHA or drill string can dissipate energy and reduce the level oftorsional oscillations.

In this idea a design principle is discussed that to the opinion of theinventors works best for damping with friction. The damping shall beachieved by a friction force where the operating point of the frictionforce with respect to the relative velocity has to be around point 204shown in FIG. 2 . This operating point leads to a high energydissipation because a friction hysteresis is achieved whereas point 202of FIG. 2 will lead to energy input into the system.

As discussed above, friction forces between the drilling system and theborehole will not generate significant additional damping in the system.This is because the relative velocity between the contact surfaces (e.g.a stabilizer and the borehole) does not have a zero mean value. The twointeracting bodies of the friction damper must have a mean velocity orrotary speed relative to each other that is small enough so that theHFTO leads to a sign change of the relative velocity of the twointeracting bodies of the friction damper. In other words, the maximumof the relative velocities between the two interacting bodies generatedby the HFTO needs to be higher than the mean relative velocity betweenthe two interacting bodies.

Energy dissipation only occurs in a slipping phase via the interfacebetween first and second elements in the damper. Slipping occurs if theinertial force exceeds the limit between sticking and slipping that isthe static friction force: F_(R)>μ₀·F_(N) (wherein the static frictionforce equals the static friction coefficient multiplied by the normalforce between both contacting surfaces). The normal force and/or thestatic or dynamic friction coefficient may be adjustable to achieve anoptimal or desired energy dissipation. Adjusting at least one of thenormal force and the static or dynamic friction coefficient may lead toan improved energy dissipation by the damping system.

As discussed herein, the placement of the friction damper should be inthe area of high HFTO accelerations, loads, and/or relative movement.Because different modes can be affected a design is preferred that isable to mitigate all HFTO modes (e.g., FIGS. 9A and 9B).

An equivalent can be used as a friction damper of the presentdisclosure. A collar 2100 with slots as shown in FIGS. 21 and 22 can beemployed. A cross-sectional view of the collar 2100 with slots is shownin FIG. 22 . In one non-limiting embodiment, the collar 2100 with slotshas a high flexibility or low stiffness and will lead to higherdeformations if no friction devices 2102 are entered. The highervelocity will cause higher centrifugal forces that will force thefriction devices 2102 that will be pressed into the slots with optimizednormal forces to allow high friction damping. In this configuration,other factors that can be optimized are the number and geometry of slotsas well as the geometry of the damper. An additional normal force can beapplied by spring elements, as shown in FIG. 22 , actuators, and/or bycentrifugal forces, as discussed above.

The advantage of this principle is that the friction devices 2102 willbe directly mounted into the force flow. A twisting of the collar due toan excited HFTO mode and corresponding mode shape will partly besupported by the friction devices 2102 that will move up and down duringone period of vibration. The high relative movement along with anoptimized friction coefficient and normal force will lead to a highdissipation of energy.

This goal is to prevent an amplitude increase of the HFTO amplitudes(represented by tangential acceleration amplitudes in this case). The(modal) damping that has to be added to every instable torsional mode bythe friction damper needs to be higher than the energy input into thesystem. The energy input is not happening instantaneously but over manyperiods until the worst case amplitude is reached (zero RPM at the drillbit).

With this concept a comparably short collar can be used because thefriction damper uses the relative movement along the distance from bit.It is not necessary to have a high tangential acceleration amplitude butonly some deflection (“twisting”) of the collar that will be achieved innearly every place along the BHA. The collar and the dampers should havea similar mass to stiffness ratio (“impedance”) compared to the BHA.This would allow the mode shape to propagate in the friction collar. Ahigh damping will be achieved that will mitigate HFTO if the parametersdiscussed above are adjusted (normal force due to springs etc.). Theadvantage in comparison to other friction damper principles is theapplication of the friction devices directly into the force flow of thedeflection to a HFTO mode. The comparably high relative velocity betweenthe friction devices and the collar will lead to a high dissipation ofenergy.

The damper will have a high benefit and will work for differentapplications. HFTO causes high costs due to high repair and maintenanceefforts, reliability issues with non-productive time and small marketshare. The proposed friction damper would work below a motor (thatdecouples HFTO) and also above a motor. It could be mounted in everyplace of the BHA that would also include a placement above the BHA ifthe mode shape propagates to this point. The mode shape will propagatethrough the whole BHA if the mass and stiffness distribution isrelatively similar. An optimal placement could for example be determinedby a torsional oscillation advisor that allows a calculation of criticalHFTO-modes and corresponding mode shapes.

Furthermore, as noted above, due to the high amplitudes at the drillbit, one location of a damper, as described herein, may be within thedrill bit. That is, in accordance with some embodiments of the presentdisclosure, the dampers may be integrated into and part of a drill bitor other disintegration device. In such embodiments, the distance-to-bitis zero or substantially zero.

In some such embodiments, a damper may be formed of a mass or inertiathat is only coupled through a damping force or damping torque to thedrill bit or a string damper element. The damping force could, forexample, and without limitation, be viscous damping, friction damping,hydraulic damping, magnetic damping (e.g., eddy current damping),piezoelectric (shunt) damping, etc. In some such embodiments, the dampermay be combined with a spring that would enable a tuned damper, forexample, a tuned friction damper. In these cases, the eigenfrequency ofthe damper would be tuned to the eigenfrequency of the mode that shallbe damped. In addition to installation or mounting within or at a drillbit (i.e., the end of a downhole string), a damper may be installed atany location in or on a BHA, and thus be arranged proximate an end ofthe downhole string.

As described above, the placement of devices for vibration damping alonga drill string affects the vibration damping efficiency. Typical HFTOmodes, because these modes are of a higher-order, have several nodes andmaxima along the BHA section of the string. Placing a vibration damper,which reacts on vibration amplitude, at a position inside or on top ofthe BHA, that has a low or no (node) amplitude of the mode shape, canlead to a low efficiency damping for the respective mode. However,placing the damper at a local maximum of the mode to be damped createshigher damping for this mode, as described above.

In accordance with some embodiments of the present disclosure, drillstring elements, hereinafter “mode-shape tuning elements,” withpredetermined or selected lengths and/or diameters may be employed toincrease a local maximum amplitude at a particular location of the modeshape, such as the mass-normalized mode shape. Such amplification canincrease the effectiveness of damping. That is, intentional and specificmodification of drill string and/or BHA can enable control of thelocation and amplitude of local maxima of the mode shape, such as themass-normalized mode shape, thereby controlling and/or improving theeffectiveness of damping, which may be implemented as described above,with the inclusion of mode-shape tuning elements.

For example, through modeling or other software, mode-shape tuningelements can be selected individually to realize improved or optimalpositioning of dampers for an individual BHA setup. Such modeling orsoftware may be used to enable custom-designed properties (e.g.,dimensions, such as length or diameter, material and/or mechanicalproperties, such as stiffness, flexibility, weight, moment of inertia,density, or modulus of elasticity (shear and bulk)) as well asposition/location of mode-shape tuning elements, and/or theposition/location of one or more damping elements. Furthermore, in someembodiments, the software/modeling may be configured to select from apool (e.g., as shown, for example, in FIG. 29A) or list of specificpreconfigured mode-shape tuning elements to be used in combination withone or more damping elements. The software/modeling might also be usedto create and optimize the pool of mode-shape tuning elements. Inaddition to length and diameter customization of mode-shape tuningelements, density, shape, modulus of elasticity (shear and bulk), and/orother parameters affecting flexibility or inertia of a string and/or BHAmay be pre-determined to control local maximum amplitude.

HFTO damping and especially placement of devices for improved oroptimized damping of HFTO is a rather new technology. The basic theoryis disclosed in Hohl et al. (2015): “Derivation and experimentalvalidation of an analytical criterion for the identification ofself-excited modes in drilling systems,” published in Journal of Soundand Vibration, 342, pp. 290-302, the contents of which are incorporatedby reference in their entirety. One presentation of mode-shape tuning tominimize vibration at certain positions in a BHA and the reduction ofexcitability S_(c) (e.g., the smallest slope of the torquecharacteristic for which the system is marginally stable) is disclosedin U.S. Pat. No. 9,976,405, titled “Method to mitigate bit inducedvibrations by intentionally modifying mode shapes of drill strings bymass or stiffness changes,” issued on May 22, 2018, the contents ofwhich are incorporated by reference in their entirety. However,artificially maximizing the amplitude of a mode shape at the actualposition of a damping element is not disclosed. For example, the use ofmode-shape tuning elements, as provided herein, may be used to amplifyor even maximize a mode shape at a specific position, and thus enableimproved efficiency of HFTO damping. Examples of mode-shape tuningelements may be torsionally soft elements (e.g., flex pipes) and/or highinertia components (e.g., heavyweight sections), or combinations of bothof various length used to amplify the amplitude of the mode shape at theposition of a damping element (e.g., a damping element as describedabove and below).

Placing dampers at arbitrary positions along a drill string is onemethod, but such arbitrary placement may lead to inefficient damping.Such arbitrary placement may be selected based on the specific BHA orother string property/characteristic, such that the dampers are placedat locations that are viable in view of other features of the string.This inefficient damping effect is a result of most positions being atsignificantly lower damping than a maximum (e.g., at locations ofnon-maxima of the mode shape, such as the mass-normalized mode shapeshown and described above). This results in the essentially-randompositioning of damping elements to result in relatively low dampingeffectiveness.

In additional to locating a damper at an inefficient location, there areoften more than one HFTO modes that are present during drillingoperation. Each mode has a respective characteristic frequency and modeshape with different local maxima and minima (depending on thewavelength). If more than one HFTO mode is likely to occur (which istypically the case), it is preferred that all (or most) modes to besufficiently damped.

FIG. 23 illustrates the mass normalized mode shapes of some example BHAHFTO modes (top plot) and normalized damping (normalized to the maximumdamping value at the distance from bit=0) for the modes (bottom plot)vs. the distance from the bit. The top plot of FIG. 23 shows that forthis BHA at least four modes are generated corresponding to frequenciesof 162 Hz, 216 Hz, 270 Hz, and 324 Hz. Maxima and minima of the fourmodes are located at different positions. For example, the first maximumof the 324 Hz mode is at approximately 10 m distance from the bit whilethe first maximum of the 270 Hz mode is at approximately 6 m distancefrom the bit. As illustrated, with the exception of the drill bit(distance 0), the damping varies with the distance from the bit but isalways below 25% of the maximum damping and is therefore rather small.As such, embodiments of the present disclosure are directed tooptimizing placement of one or more dampers at effective positions alongor preferably on top of the BHA to effectively dampen or reduce all BHAHTFO modes. For example, depending on the position of the one or moredampers with respect to the BHA (e.g., if one or more dampers arelocated outside of the BHA or at the top or the bottom of the BHA),advantageously, the use of a damper element or a damper element subwithout electrical connection and/or a damper element or a damperelement sub that is not wired from the top to the bottom of the damperelement or the damper element sub may be possible.

Embodiments of the present disclosure are directed to the placement ofdampers and the tuning of mode shapes to obtain acceptable damping forall modes which are likely to occur during drilling with a specific BHAsetup. In order to capture all potential mode shapes, damper elementsare not necessarily placed at the maximum position of each mode, but atpositions showing acceptable amplitudes of the mode shape to createsufficient damping. As such, a compromise across all modes andpositioning together with selection of applicable mode-shape tuningelements (e.g., flex and heavyweight sections) to amplify andconcentrate local maxima to certain positions is defined. Under theassumption of the susceptibility or severity of certain modes, aweighting of certain modes can be conducted to optimize damping ofselected or target modes.

Turning to FIGS. 24A-24C, schematic plots illustrating the placement ofa damper on a drill string and/or BHA are shown. FIGS. 24A-24C representthe placement of a single damper for a single HFTO mode. However, itwill be appreciated that the described process may be employed for anynumber of damper elements and modes. In FIG. 24A, a random placement ofthe damper is employed, and this random placement only achieves adamping D of about 20% of the maximum possible damping of a damper at anoptimal position in a non-optimized BHA (e.g., a BHA that is notoptimized with respect to dimensions, such as length or diameter,material and/or mechanical properties, such as stiffness, flexibility,weight, moment of inertia, density, or modulus of elasticity (shear andbulk) as well as position/location). Although the mass-normalizeddeflection of the mode is only slightly smaller than 50% compared tooptimal positioning, the resulting damping is significantly smaller dueto the quadratic influence of the positioning (mass-normalized modeshape φ_((i,j)) for mode i and position j on the damping effect (D isproportional to φ_((i,j)) ²). Such relationship is described in theabove incorporated U.S. Pat. No. 9,976,405.

One method for enabling optimization for the placement of a damper is tochange the length of various drill string elements near the damper. Forexample, by lengthening a tube, the damper can be moved toward a maximumof a mode shape (shown in FIG. 24B), leading to an increase of thedamping effect (i.e., optimum position within the initial BHA). Thelength of elements may be increased by the inclusion of one or moremode-shape tuning elements in a string and/or replacing a conventionalstring element with a mode-shape tuning element. The resulting dampingcan reach efficiency of up to 100% (i.e., complete damping of a givenHFTO mode due to placement of a damper and mode-shape tuning/shiftingdue to the mode-shape tuning elements).

In addition to length alterations, one or more mode-shape tuningelements may be used to change the moment of inertia of the string. Thisenable local increases in the amplitude of the mode shape(s) bycombining soft and high inertia drill string components. FIG. 24Cillustrates the position of a damper within a BHA when two componentshave been changed in length and diameter (i.e., replaced by mode-shapetuning elements), compared to the maximum damping without the mode-shapetuning elements includes, the position of the damper results in 140% ofthe maximal damping of a BHA that is not optimized with respect todimensions, such as length or diameter, material and/or mechanicalproperties, such as stiffness, flexibility, weight, moment of inertia,density, or modulus of elasticity (shear and bulk) as well asposition/location. That is, using mode-shape tuning elements of specificelement length and diameter for position optimization relative to agiven mode maximum, more than 100% maximum damping is possible.

The mode-shape tuning elements of the present disclosure enable localchanges in the properties of drill string and/or the BHA. The mode-shapetuning elements can be used as additional elements to a string or may beused as replacements of a typical string or BHA component. Themode-shape tuning elements allow for selection of diameter, length,density, modulus of elasticity, material, geometry, cross-sectionalgeometry, etc., to tune or shift a mode shape, and thus enable the useof dampers in specific locations to result in maximum dampingeffectiveness. The use of mode-shape tuning elements may result inchanges of the mode shapes (e.g., the amplitude) of one, several (e.g.,for the critical modes), or all modes locally at the position of thedamper as well as the whole mode (e.g., at the drill bit). Further, theuse of mode-shape tuning elements may change the frequency of the one,several, or all modes (e.g., modes can become critical or uncritical).Moreover, mode-shape tuning elements can change the excitability of one,several, or all modes (e.g., modes can become critical or uncritical).For example, the combination of torsionally soft mode-shape tuningelements (e.g., flex pipes) in combination with high inertia components(e.g., heavyweight sections) of various length, can amplify theamplitude of the mode shape at the position of the damping element.

For this reason, optimization methods of the present disclosure can beused to determine the damping achieved by one or numerous dampers withrespect various modes. By changing local components (e.g., replacingcomponents with one or more mode-shape tuning elements), not only thedamping effect is influenced by the placement, but also the excitabilityof the critical modes may be affected as well.

Optimization methods that may be employed in accordance with embodimentsof the present disclosure may include analyzing/calculating/simulating(e.g., numerically simulating) one or more HFTO modes of a BHA or adrilling system to determine maxima of mode shapes or dampingefficiency. In a second step, a damper and/or a mode-shape tuningelement with a given characteristic may be selected. Suchcharacteristics may include, without limitation, dimensions, such aslength or diameter, material and/or mechanical properties, such asstiffness, flexibility, weight, moment of inertia, density, or modulusof elasticity (shear and bulk). A position will be selected where thedamper and/or a mode-shape tuning element will be added to the BHA togenerate a modified BHA. In a next step, the modified BHA will beanalyzed/calculated/simulated (e.g., numerically simulated) to estimateone or more HFTO modes of the modified BHA to determine modified maximaof mode shapes or modified damping efficiency. If the modified BHA meetsa criterion (e.g., a preselected criterion, such as a threshold valuethat is related to a maximum mode shape, an excitability, a mode shapederivative, a damping efficiency, or a difference of two mode shapeamplitudes), the modified BHA may be used to drill a borehole sectioninto the formation. Otherwise, the modified BHA may be further modifiedby adding/removing/moving damper(s) and/or a mode-shape tuning elementwith a given characteristic until the criterion is met. Thus, abeneficial placement and selection of dampers and mode-shape tuningelements may be determined by an iterative process.

In an additional or alternative embodiment, the beneficial placement andselection of dampers and mode-shape tuning elements may be determined bya (numerical) inversion method. Such inversion method may include, forexample, an automatic or semi-automatic inversion method. Further, in anadditional or alternative embodiment, the beneficial placement andselection of dampers and mode-shape tuning elements may be determined byoptimization methods that may include, without limitation,gradient-based optimization. Such gradient-based optimization mayinclude Nelder Mead. Other possible optimization methods are Monte Carlosimulations, Levenberg-Marquard optimization, genetic algorithm,simulated annealing, least-squares-algorithm, ant-colony-optimizationalgorithm, conjugate gradient method, Krylov-subspace-method,biconjugate gradient method, or any other optimization method as will beappreciated by those of skill in the art. The optimization criteria orpenalty function is primarily set up to maximize damping, but aconstrained optimization of geometric factors or a set of predefinedmode-shape tuning elements or other constraints can be used.Advantageously, one, several, or all modes may be weighted by aweighting factor or weighting function during the optimization, forexample, to determine the optimization criteria or penalty function. Itwill be appreciated that both the mode-shape tuning and the location andeffect of damping elements may be considered for a designedapplication/configuration.

Turning now to FIG. 25 , an illustration of mode shapes as well as thenormalized minimum damping of four (4) modes is shown. In theconfiguration used to illustrate FIG. 25 , one or more mode-shape tuningelements are used in the BHA to shift or change the location of themaxima (e.g., as compared to that shown in FIG. 23 ). As shown in FIG.25 , at about a distance of 7.5 m from the drill bit, a minimalnormalized damping of more than 60% can be determined for all modes.Therefore, this position is very suitable for a damper to stabilize allmodes. That is, by using mode-shape tuning elements, the position ofmaxima of multiple different modes may be substantially aligned,allowing for a damper (or a few dampers) to reduce HFTO of a string.

Furthermore, still referring to FIG. 25 , if not one but two dampers areto be installed in the drill string, the position at 18 m from the drillbit can also be considered as a good position because of the alignmentof the different maxima. However, the minimum normalized damping at thenew position (18 m) may be small compared to the damping at the 7.5 mposition, the combination of both positions may offer improved dampingas compared to a single-damping system. Two modes (the one at 218 Hz andat 263 Hz) have high deflections of the mode shapes at 7.5 m and twomodes (160 Hz and 317 Hz) have high deflections of the mode shapes at 18m. As a result, placement of damper elements at 7.5 m and 18 m from thedrill bit may result in all modes being damped.

To enable the mode-shape tuning, one or more structural elements may beadded to a drill string or BHA or may be used to replace atypical/conventional part with a modified part that is a mode-shapetuning element. That is, by including one or more mode-shape tuningelements, a tool string (i.e., drilling string plus BHA) may becustomized such that one or more maxima associated with HFTO may beshifted in location, and multiple different maxima may be shifted to asingle location or proximate a single location, such that a singledamper element may be used to damp HTFO of different modes or orders.The mode-shape tuning elements may include, for example, an iron pipesection of a selected or predetermined length, diameter, and/orgeometry, that is attached to the drill string proximate the BHA. Thismode-shape tuning element may add additional weight and/or flexibility(or inflexibility) to the drill string at the location it is connected,thus altering (and shifting) the maxima of HTFO of the system. Based onthis shift, a damper element may be installed to damp one or moreselected HFTO modes.

Advantageously, mode-shape tuning elements added to a section of thedrill string, outside, at, in, or on the BHA, may be used to shift thelocation of HFTO maxima and enable one or more damper elements toprovide improved damping efficiency. The position of the mode-shapetuning elements with respect to the BHA may advantageously allow the useof mode-shape tuning elements without electrical connection and/ormode-shape tuning elements that are not wired from the top to the bottomof the mode-shape tuning element. The performance of actual damperelements can drastically be increased through the inclusion ofmode-shape tuning elements, which in turn can lead to fewer damperelements required. Further, such optimization or improved efficiency canlead to the use of smaller and/or cheaper damper elements and betterdamping across various modes.

It will be appreciated that embodiments of the present disclosure arenot only directed to improving the position of a damper with respect toa specific mode shape. That is, embodiments of the present disclosureare directed to changing properties of drill string elements and/orcomposition within or proximate the BHA. Such modifications improve theperformance of installed dampers according to positioning andmodification of the mode shape (i.e., mode-shape tuning, adjustment,and/or shifting). By changing one or more characteristics or properties(e.g., length, diameter, density, geometry, etc.) of a string, improveddamping (e.g., more than 100%) can be achieved for one or more HFTOmodes.

Turning to FIGS. 26A-26B, illustrations of a downhole string 2600 havingtwo dampers are shown. FIG. 26A is a schematic structural illustrationof the downhole string 2600 and FIG. 26B illustrates the modified ortuned mode shapes by incorporating mode-shape tuning elements 2602. Asshown, in this embodiment, two damper elements 2604 are shown, locatedat shifted maxima such that multiple HFTO modes may be damped by thedamper elements 2604. In this illustration the downhole string 2600represents a sample BHA having damper elements 2604 installed thereon.BHAs are subject to critical vibration environments, and thus damping ofsuch vibrations is advantageous. For all BHA configurations only fewmode-shape tuning elements 2602 (e.g., flex and heavyweight pipesegments) are required for maximum damping impact placement of thedamper elements 2604.

In accordance with some embodiments of the present disclosure, it may bepossible to permanently achieve a specific response for all HFTO modesat a position by using certain components (e.g., mode-shape tuningelements, specific damper elements, isolator elements, etc.). Forexample, isolator elements are shown and described in commonly ownedU.S. Patent Application Publication No. 2019/0284882A1, entitled“Dampers for mitigation of downhole tool vibrations and vibrationisolation device for downhole bottom hole assembly,” U.S. ProvisionalPatent Application 62/899,331, entitled “Vibration Isolating Coupler forReducing High Frequency Torsional Vibrations in a Drill String,” andU.S. Provisional Patent Application 62/899,332, entitled “VibrationIsolating Coupler for Attenuating Vibrations in a Drill String,” whichare incorporated herein by reference in their entireties. Moreover, itwill be appreciated that such mode-shape shifting and tuning is notlimited to friction dampers. For example, stiffness-based dampingprinciples may be employed in accordance with some embodiments of thepresent disclosure. The optimal position of stiffness-based dampingprinciples does not depend on the amplitude of the mode shape, but onthe derivative thereof. As such, the difference between two amplitudesof the mode shape (mode shape difference) may be considered forstiffness-based damping. An optimum for a damping principle based onstiffness are nodes, since the relative displacement is greatest there.

As noted above, in addition to adding length and/or weight in the formof mode-shape tuning elements, the mode-shape tuning elements of thepresent disclosure may provide other modifications to a string and/orBHA such that a mode shape is shifted or tuned to a specific location,thus enabling improved efficiency of damper elements installed on or inthe string and/or BHA. For example, lengthening pipe segments may beused to increase flexibility of a string, modified shapes or geometry(other than just changing diameter) may be employed, altering densityand/or modulus of elasticity, or other property of a string/BHA may bemodified or customized to achieve a shift in HFTO mode shape. As such, acombination of mode-shape tuning elements and damper elements may beemployed in a downhole system to improve the efficiency of HFTO dampingand thus reduction in tool vibrations and adverse impacts associatedtherewith may be reduced, avoided, or eliminated.

Turning now to FIGS. 27-28 , schematic illustrations of damper elements2700, 2800 are shown. The damper elements 2700, 2800 are configured forinstallation within a blade of a disintegration device, as describedabove. Each damper element 2700, 2800 includes a respective housing2702, 2802 for housing and containing the components of the respectivedamper elements 2700, 2800. A first damper element 2700 has asubstantially rectangular geometry (with curved corners) and a seconddamper element 2800 has a substantially circular geometry. The housings2702, 2802 are configured to installation into blades of adisintegration device (e.g., as shown in FIG. 26 ).

The damper elements 2700, 2800 each include a mass element 2704, 2804movably mounted within the housings 2702, 2802. The mass element 2704,2804 is arranged between a mounting element 2706, 2806 and a contactelement 2708, 2808. The mounting elements 2706, 2806 are configured toapply a force upon the respective mass element 2704, 2804 toward thecontact elements 2708, 2808. As such, a frictional contact may beachieved between the respective mass element 2704, 2804 and the contactelements 2708, 2808. The mass elements 2704, 2804 may be arranged withone or more limit stops 2710, 2810 within the respective housings 2702,2802. The limit stops 2710, 2810 may include optional stiffness orhydraulic elements for damping of the movement of the mass elements2704, 2804,

Furthermore, the limit stops 2710, 2810 may prevent the mass elements2704, 2804 from being stuck in one edge of the housing 2702, 2802. Thelimit stops 2710, 2810 can be configured with springs or other elementsto avoid damage to the mass elements 2704, 2804 and to urge the masselements 2704, 2804 toward a middle or rest position relative to thehousing. In some embodiments, it may be beneficial to optimize a springstiffness and/or gap in the housing 2702, 2802 to allow the masselements 2704, 2804 to move within the housing 2702, 2802. The damperelements 2700, 2800 may be arranged as inserts (e.g., the housing 2702,2802 is configured for installation). The insertable damper elements2700, 2800 may be installed such that the mass elements 2704, 2804 areplaced at a position of high radius with respect to an axis of adrilling system, to increase the rotational inertia.

The mounting element 2706, 2806 are configured to apply a normal forceupon the mass elements 2704, 2804 (e.g., a force that is normal tomounting element 2706, 2806 or mass elements 2704, 2804). For example,the mounting element 2706, 2806 may be arranged as spring shells to urgethe mass elements 2704, 2804 into contact with the contact element 2708,2808. Furthermore, the mounting elements 2706, 2806 and/or the contactelements 2708, 2808 can be configured to control a tangential movementof the mass elements 2704, 2804 to enable damping of HFTO. In someembodiments, the mounting elements 2706, 2806 urge the mass elements2704, 2804 into contact with the contact element 2708, 2808 to generatea friction force. The friction force is applied, for example, through amaterial that is beneficial with respect to the friction coefficient andthe expected wear that should be as low as possible.

In accordance with embodiments of the present disclosure, integration ofdamping into the drill bit or other location along the string (e.g., ator in a BHA) may be achieved. The damping may be applied by any axial,tangential, and/or radial force or corresponding torque that is able todissipate energy. In case of coupled modes, damping forces in an axialdirection is also able to dissipate energy from the torsional direction.Coupling could also be achieved kinematically, such as, through thebit-rock interaction. As described for friction damping, contactingsurfaces applied with a friction coefficient and normal force may beoptimized and/or selected for damping one or more critical modes. Insome embodiments, beneficial materials or designs may be employed toprevent wear (e.g., copper or polycrystalline diamond cutters). Multiplecontacts with different properties could be used to tune the system to abeneficial friction coefficient or characteristic.

Another form of damping that may be employed is hydraulic damping. Suchhydraulic damping may be implemented through a system, whether in thebit blades, or arranged about or in other locations of a drill bit ordisintegration device or along a BHA or downhole string. One example ofa hydraulic damper is shown and described in commonly owned U.S. PatentApplication No. 62/899,291, entitled “Viscous Vibration Damping ofTorsional Oscillation” which is incorporated herein by reference in itsentirety. In some such embodiments, a viscous fluid (e.g., viscous fluidin chambers) may be arranged and installed in similar locations asdescribed above. In some such applications, the (shear) stresses in thefluid between an inertia ring/mass and the drill bit/drilling system maybe selected to achieve a (damping) force that acts in the direction ofthe tangential acceleration and associated harmonic movement to damptorsional oscillations, such as HFTO. In the case of ring shearing, thefluid provides a damping force between the inertia ring/mass and thedrill bit. In this case, the ring may require a closed housing and,potentially, a well-defined geometry of the gaps between the ring andthe housing. In hydraulic damping, the viscous damping forces aresensitive to parameter changes of the gaps and the viscous fluid.Therefore, a temperature insensitive fluid or a fluid that is lesssensitive to temperature may be preferred. Fluids with different shearstresses as a function of the shear rate can be used to achieve abeneficial behavior. Some such example fluids include, withoutlimitation, Newtonian fluids, dilatant (e.g., shear-thickening fluids),pseudoplastic, Bingham plastic, Bingham pseudoplastic fluids, etc.Advantageously, solids may be added to the fluid to achieve dispersivebehavior of the fluid.

Further, in some embodiments, magnetic damping can be employed. Magneticdamping may be achieved by a permanent magnet (e.g., mounted on aninertia ring/mass) that is allowed to move relative to a coil and can beused to damp HFTO. Depending on the magnetic principle, the dampingforce characteristic is similar to hydraulic (e.g., eddy current) orfriction (Hysteresis) forces. In some such configurations, the forcewould act in the direction of the tangential acceleration or any otherdirection that is able to lead to damping in the circumferentialdirection or the direction that should be damped.

Furthermore, in some embodiments, piezoelectric damping principles maybe employed to prevent torsional oscillations, such as HFTO at the drillbit or in the drill string. A piezoelectric material that is connectedto an inertia ring/mass on one side and to a portion of a downholestring on the other side can be used. The electrodes of thepiezoelectric material can be connected to a circuit incorporatingcoils, resistors, and capacitances or semi-active or active components.A combination of the electrical components can be used to achievebeneficial damping characteristics between the inertia ring/mass and thecomponents of a downhole string. A circuit could be adjusted to naturalfrequency of the system to work as a tuned damper (i.e., for one or moredesired modes). A resistor could be arranged to directly dissipateenergy if the piezoelectric stack is deformed by the relative forcebetween the inertia ring/mass and the downhole string component.Additionally, the stiffness of the piezoelectric material and theinertia ring/mass could be tuned to a specific frequency as well. Theelectrodes of the piezoelectric material can be arranged to damptorsional vibrations. The direction of the damping forces can bedifferent from the direction of the electrodes using the beneficialtransformation effect from mechanical force-to-electrical signal that issuggested by the design of the piezoelectric actor. Well-known effectsof piezoelectric coefficients are D₃₃ (in a direction of the force), D₃₁(orthogonal to a direction of the force), and D₁₅ (shear stresses). Theplacement of the piezoelectric material can be placed to optimize orcontrol the coupling between the mechanical and the electrical systemfor a specific mode or multiple mode shapes that are critical to HFTO.Further, various different materials that transfer mechanical force orstress or related loads into electrical signals can be used withoutdeparting from the scope of the present disclosure.

In addition, the internal damping and the resulting forces of materialscan be used to reduce HFTO. That is, material damping can be achievedpassively through the damping properties of high damping materials. Somesuch materials may include, without limitation, polymers, elastomers,rubber, etc. as well as the damping effect of multifunctional materialssuch as shape memory alloys. The material properties of some materials,such as shape memory alloys, can be actively influenced or controlled toachieve greater damping effects.

Other damping configurations are possible without departing from thescope of the present disclosure. For example, negative capacitances andsemi-active components using switching techniques may be employed.Additional damping techniques and components may be used, and the abovedescribed embodiments and variations are provided for illustrative andexplanatory purposes and are not intended to be limiting. All of thedamping principles described herein can be adjusted to work as a tuneddamper by adding mechanical springs adjusted to a specific frequency andby adding damping of any type. Further, one or more of the dampingprinciples described herein (or other methods/mechanisms) can becombined in a multi-principle configuration. For example, ring-typedampers or tangential mass/inertia dampers may be installed within orattached to blades of a disintegration device or at other locationswithin the drill string. Furthermore, magnetic, hydraulic, friction,piezoelectric, and material damping forces and principles could becombined to achieve a robust damping effect, such as, for example, withrespect to temperature.

As described above, one or more damper elements may be integrated into adrill bit or other disintegration device or at other locations along adownhole string or a BHA. For example, a bit damper may be positioned inor about a drill bit shank. In some configurations, a damper inertiaring could be lubricated by mud or covered by a sleeve design. In someconfigurations, a closed or uninterrupted ring may be employed. In otherconfigurations, partial arcs may be assembled about a downhole string(e.g., could be mounted if ring cannot be assembled otherwise). In somesuch embodiments, two half-ring arcs may be employed. In otherembodiments, more than two ring arcs may be used to form a complete hoop(circumferential) structure or less than a complete hoop(circumferential) structure, depending on the specific configurationthat is implemented.

In some embodiments, a broken-ring structure may be employed, wherediscrete masses are arranged behind or adjacent to blades of a drillbit. In another example, a full ring-structure may be arranged adjacentthe blades, but specific additional mass elements or features of thering may be located relative to the specific blades of the drill bit.One such example may have a relatively thick ring at a location of theblades and lower thickness to allow a flow of cuttings to pass along thedrill bit. Further, such rings may be located at other locations along adownhole string (e.g., BHA).

In some embodiments, limit stop may be provided and may prevent theinertia ring/mass to move freely about the circumference of a drill bit.Such limit stop may be provided in embodiments where the mass or highermass is located behind or adjacent specific blades. In such cases, thelimit stop may ensure that the inertia ring/mass remains in positionrelative to the blades or that the space in which the inertia ring/masscan move is limited.

It will be appreciated that friction-type damper elements of the presentdisclosure may employ radial and/or axial contact forces to achievecircumferential friction forces. Radial friction forces could beachieved by springs, pressure differences, or by an elastic design of aninertia ring or ring segments that may have two or more shells and maybe pre-stressed. An axial normal force can be achieved by springs,pressure differences, and/or a weight of inertia ring/mass in anon-horizontal borehole. The material of the drill bit or otherdisintegration device may be steel or matrix composite, etc. In someembodiments, a bearing may be used in a radial direction to guaranteethe movement of the inertia ring/mass. That is, a bearing may beprovided to support circumferential or tangential movement of a damperelement. An axial bearing may be used to decouple a potential normalforce spring stack from rotational movement.

In some embodiments, alternatively from a ring-type damper element, orin combination therewith, damper elements may be implemented in or onblades of a disintegration device, a stabilizer, or in or on othercomponents of the downhole string. In some such embodiments, the damperelements may be installed within housings that are screwed into theblades or recesses, under cover sleeves, or hatch covers. In some suchconfigurations, one or more limit stops may be provided to prevent thedamper elements from sticking or wedging into an edge or corner of thehousing. Contact between the limit stop and a mass of the damper may beachieved using springs or other biasing elements or structures. In someembodiments, the spring stiffness or a gap in the housing may beselected to allow the mass of the damper to move within the housing, andthus enable damping of vibrations, as described above.

Adjustment elements that change the properties of the contact betweenthe contacting elements in the downhole string may also be employed. Forexample, the normal force may be adjusted in a frictional contact.Further, the normal force, or the efficiency of the damper could bemeasured by load and acceleration or other vibration measurement sensingdevices and adjusted based on these measurements.

Turning now to FIGS. 29A-29B, schematic illustrations of various typesof mode-shape tuning elements are shown. FIG. 29A illustrates a set ofexample mode-shape-tuning elements 2902-2916 and FIG. 29B illustrates adownhole string 2920 (e.g., a BHA) having various mode-shape tuningelements 2922 (e.g., one or more of example mode-shape-tuning elements2902-2916) installed thereon in order to tune or shift or reduce one ormore maxima of a HFTO mode and thus enable damping of such HFTOvibrations within the downhole string 2920.

As shown in FIG. 29A, the mode-shape-tuning elements can have variousdimensions. Each of mode-shape-tuning elements 2902-2916 has a differentlength and as shown, mode-shape-tuning elements 2902, 2904 have largerdiameters and may be configured as weight-adding (i.e., heavy weight)mode-shape-tuning elements. In contrast, mode-shape-tuning elements2906, 2908, 2910, 2912, 2914, 2916 are each narrower in diameter and mayprovide flexibility to a string to which they are attached (i.e., flexpipes). Mode-shape-tuning elements 2902-2916 may also be different instiffness with respect to torsional twist. Also shown in FIG. 29A is adamper element sub 2918. A downhole string, such as the downhole string2920 shown in FIG. 29B, may be configured with one or moremode-shape-tuning elements to enable shifting of one or more maxima ofHFTO, and then enable improved damping to be provided by the damperelement sub 2918.

As shown in FIG. 29B, the downhole string 2920 includes a motor 2924,one or more of mode-shape-tuning elements 2922 (which, for example, maybe selected from the mode-shape-tuning elements 2902-2916 shown in FIG.29A), a damper element sub 2918, a flex stabilization sub 2926, a set ofdrilling operation elements 2928 (e.g., measurement-while-drilling,logging-while-drilling, steering unit, etc.), and a disintegrationdevice 2930 (e.g., a drill bit) disposed on an end thereof. Theinclusion of the mode-shape-tuning elements 2922 in the downhole string2920 enables tuning or shifting of one or more maxima of HFTO, and thusHFTO may be reduced where elements are located within the BHA that aresensitive with respect to HFTO. In addition, the inclusion of themode-shape-tuning elements 2922 in the downhole string 2920 enablestuning or shifting of one or more maxima of HFTO, such as location ofdamping element sub 2918 may be optimized to damp such vibrations.

Accordingly, embodiments of the present disclosure are directed tolocating a damping system, such as a ring-type damper or tangentialdamper, in a downhole string, such as at or in a drill bit or otherdisintegration device or at other specific locations in/on/along thedownhole string. By locating the damping system at specific locationsin/on/along the downhole string (e.g., in the steering unit, in thedrill bit, or at other locations), improved damping of HFTO or othervibration modes may be achieved. Further, mode-shape tuning elements maybe configured to enable placement of one or more damping elements at ornear the end of the drill string, the end of the BHA, close to or at thedrill bit (for example within 10 m of the drill bit, such as within 5 mof the drill bit or even within 3 m of the drill bit), at one or moremaxima of or more mode shapes, or at one or more mode shape nodes toefficiently enable damping of one or more HFTO modes with one dampingelement. That is, as described herein, the maximum of multiple differentHFTO modes may be aligned (tuned) to enable optimum placement of adamping element to damp one or more HFTO modes and thus reduce downholesystem vibrations.

Embodiment 1: A system for damping high frequency torsional oscillations(HFTO) of a downhole system, the downhole system comprising: a downholedrilling system disposed at an end of the downhole system in operativeconnection with a drill bit; a damping system installed on the downholedrilling system, the damping system comprising at least one damperelement configured to dampen at least one HFTO mode; and at least onemode-shape tuning element arranged on the drilling system, wherein theat least one mode-shape tuning element is configured and positioned onthe drilling system to modify at least one of a shape of the HFTO mode,a frequency of the HFTO mode, an excitability of the HFTO mode, and adamping efficiency of the at least one damper element.

Embodiment 2: The system according to any preceding embodiment, whereinthe at least one mode-shape tuning element is configured and positionedon the drilling system to modify the shape of the HFTO mode at aposition of the at least one damper element.

Embodiment 3: The system according to any preceding embodiment, whereinthe at least one mode-shape tuning element is selected based on at leastone of a dimension of the at least one mode-shape tuning element, amaterial property of the at least one mode-shape tuning element, and amechanical property of the at least one mode-shape tuning element.

Embodiment 4: The system according to any preceding embodiment, whereinthe positioning of the at least one mode-shape tuning element on thedrilling system is selected to at least one of modify the shape of theHFTO mode at a position of the at least one damper element and optimizethe damping efficiency of the at least one damper element.

Embodiment 5: The system according to any preceding embodiment, furthercomprising a pool of mode-shape tuning elements from which the at leastone mode-shape tuning element is selected for arrangement on thedrilling system.

Embodiment 6: The system according to any preceding embodiment, whereinthe at least one mode-shape tuning element is selected for thearrangement on the drilling system based on a numeric simulation of theHFTO of at least a portion of the downhole system.

Embodiment 7: The system according to any preceding embodiment, whereinat least one of the at least one damper element and the at least onemode-shape tuning element is positioned and/or selected based on anumeric inversion.

Embodiment 8: The system according to any preceding embodiment, whereinthe damping system is at least one of a viscous damping system, afriction damping system, a hydraulic damping system, a magnetic dampingsystem, and a piezoelectric damping system.

Embodiment 9: The system according to any preceding embodiment, furthercomprising an isolator.

Embodiment 10: The system according to any preceding embodiment, whereinthe at least one damper element is arranged within 10 m of the drillbit.

Embodiment 11: A method for damping high frequency torsionaloscillations (HFTO) of a downhole system, the method comprising:drilling with a downhole drilling system into the earth's subsurface,wherein the downhole drilling system is in operative connection with adrill bit and comprises a damping system that includes at least onedamper element and at least one mode-shape tuning element arranged onthe drilling system; configuring and positioning the at least onemode-shape tuning element on the drilling system to modify at least oneof a shape of the HFTO mode, a frequency of the HFTO mode, anexcitability of the HFTO mode, and a damping efficiency of the at leastone damper element; and damping at least one HFTO mode with the at leastone damper element.

Embodiment 12: The method according to any preceding embodiment, whereinthe at least one mode-shape tuning element is configured and positionedon the drilling system to modify the shape of the HFTO mode at aposition of the at least one damper element.

Embodiment 13: The method according to any preceding embodiment, furthercomprising selecting the at least one mode-shape tuning element for thearrangement in the drilling system based on at least one of a dimensionof the at least one mode-shape tuning element, a material property ofthe at least one mode-shape tuning element, and a mechanical property ofthe at least one mode-shape tuning element.

Embodiment 14: The method according to any preceding embodiment, furthercomprising selecting a position of the at least one mode-shape tuningelement on the drilling system to at least one of modify the shape ofthe HFTO mode at a position of the at least one damper element andoptimize the damping efficiency of the at least one damper element.

Embodiment 15: The method according to any preceding embodiment, furthercomprising selecting the at least one mode-shape tuning element from apool of mode-shape tuning elements for the arrangement in the drillingsystem.

Embodiment 16: The method according to any preceding embodiment, furthercomprising: executing a numeric simulation of the HFTO of at least aportion of the downhole system; and selecting the at least onemode-shape tuning element for the arrangement in the drilling systembased on the numeric simulation of the HFTO of the portion of thedownhole system.

Embodiment 17: The method according to any preceding embodiment, furthercomprising: executing a numeric inversion; and at least one ofpositioning and selecting at least one of the at least one damperelement and the at least one mode-shape tuning element based on thenumeric inversion.

Embodiment 18: The method according to any preceding embodiment, whereinthe damping system is at least one of a viscous damping system, afriction damping system, a hydraulic damping system, a magnetic dampingsystem, and a piezoelectric damping system.

Embodiment 19: The method according to any preceding embodiment, whereinthe downhole drilling system further comprises an isolator.

Embodiment 20: The method according to any preceding embodiment, whereinthe at least one damper element is arranged within 10 m of the drillbit.

Embodiment 21: A system for damping torsional oscillations of downholesystems, the system comprising: a drilling system comprising abottomhole assembly disposed on the end of a drill string; at least onemode-shape tuning element arranged on the drilling system, the at leastone mode-shape tuning element configured to shift the location of one ormore maxima of a high-frequency torsional oscillations (HFTO) mode; anda damping system configured on the drilling system, the damping systemcomprising at least one damper element arranged more close to theshifted location of the one or more maxima then without the mode-shapetuning element arranged on the drilling system.

Embodiment 22: The system of any preceding embodiment, wherein the atleast one mode-shape tuning element is a section of pipe having at leastone of, a predefined dimension, such as a predefined length orpredefined diameter, material and/or predefined mechanical properties,such as a predefined stiffness, predefined flexibility, predefinedweight, predefined moment of inertia, predefined density, or predefinedmodulus of elasticity (shear and bulk) as well as predefinedposition/location.

Embodiment 23: The system of any preceding embodiment, wherein thedamping system comprises a damping element sub that houses the at leastone damper element.

Embodiment 24: The system of any preceding embodiment, wherein thedamping system is configured to provide at least one of viscous damping,friction damping, hydraulic damping, piezoelectric damping, eddy currentdamping, and magnetic damping of torsional oscillations of the drillingsystem.

Embodiment 25: A method of damping torsional oscillations of a downholesystem in a borehole, the method comprising: installing at least onemode-shape tuning element on a drilling system, the at least onemode-shape tuning element configured to shift the location of one ormore maxima of a high-frequency torsional oscillations (HFTO) mode ofthe drilling system; and installing a damping system on the drillingsystem, the damping system comprising at least one damper elementarranged more close to the shifted location of the maxima then withoutthe mode-shape tuning element installed on the drilling system.

Embodiment 26: The method of any preceding embodiment, wherein the atleast one mode-shape tuning element is a section of pipe having at leastone of predefined dimensions, such as a predefined length or predefineddiameter, material and/or predefined mechanical properties, such as apredefined stiffness, predefined flexibility, predefined weight,predefined moment of inertia, predefined density, or predefined modulusof elasticity (shear and bulk) as well as predefined position/location.

Embodiment 27: The method of any preceding embodiment, wherein thedamping system comprises a damping element sub that houses the at leastone damper element.

Embodiment 28: The method of any preceding embodiment, wherein thedamping system is configured to provide at least one of viscous damping,friction damping, hydraulic damping, piezoelectric damping, eddy currentdamping, and magnetic damping of torsional oscillations of the drillingsystem.

In support of the teachings herein, various analysis components may beused including a digital and/or an analog system. For example,controllers, computer processing systems, and/or geo-steering systems asprovided herein and/or used with embodiments described herein mayinclude digital and/or analog systems. The systems may have componentssuch as processors, storage media, memory, inputs, outputs,communications links (e.g., wired, wireless, optical, or other), userinterfaces, software programs, signal processors (e.g., digital oranalog) and other such components (e.g., such as resistors, capacitors,inductors, and others) to provide for operation and analyses of theapparatus and methods disclosed herein in any of several mannerswell-appreciated in the art. It is considered that these teachings maybe, but need not be, implemented in conjunction with a set of computerexecutable instructions stored on a non-transitory computer readablemedium, including memory (e.g., ROMs, RAMs), optical (e.g., CD-ROMs), ormagnetic (e.g., disks, hard drives), or any other type that whenexecuted causes a computer to implement the methods and/or processesdescribed herein. These instructions may provide for equipmentoperation, control, data collection, analysis and other functions deemedrelevant by a system designer, owner, user, or other such personnel, inaddition to the functions described in this disclosure. Processed data,such as a result of an implemented method, may be transmitted as asignal via a processor output interface to a signal receiving device.The signal receiving device may be a display monitor or printer forpresenting the result to a user. Alternatively, or in addition, thesignal receiving device may be memory or a storage medium. It will beappreciated that storing the result in memory or the storage medium maytransform the memory or storage medium into a new state (i.e.,containing the result) from a prior state (i.e., not containing theresult). Further, in some embodiments, an alert signal may betransmitted from the processor to a user interface if the result exceedsa threshold value.

Furthermore, various other components may be included and called uponfor providing for aspects of the teachings herein. For example, asensor, transmitter, receiver, transceiver, antenna, controller, opticalunit, electrical unit, and/or electromechanical unit may be included insupport of the various aspects discussed herein or in support of otherfunctions beyond this disclosure.

The use of the terms “a” and “an” and “the” and similar referents in thecontext of describing the invention (especially in the context of thefollowing claims) are to be construed to cover both the singular and theplural, unless otherwise indicated herein or clearly contradicted bycontext. Further, it should be noted that the terms “first,” “second,”and the like herein do not denote any order, quantity, or importance,but rather are used to distinguish one element from another. Themodifier “about” used in connection with a quantity is inclusive of thestated value and has the meaning dictated by the context (e.g., itincludes the degree of error associated with measurement of theparticular quantity).

It will be recognized that the various components or technologies mayprovide certain necessary or beneficial functionality or features.Accordingly, these functions and features as may be needed in support ofthe appended claims and variations thereof, are recognized as beinginherently included as a part of the teachings herein and a part of thepresent disclosure.

The teachings of the present disclosure may be used in a variety of welloperations. These operations may involve using one or more treatmentagents to treat a formation, the fluids resident in a formation, aborehole, and/or equipment in the borehole, such as production tubing.The treatment agents may be in the form of liquids, gases, solids,semi-solids, and mixtures thereof. Illustrative treatment agentsinclude, but are not limited to, fracturing fluids, acids, steam, water,brine, anti-corrosion agents, cement, permeability modifiers, drillingmuds, emulsifiers, demulsifiers, tracers, flow improvers etc.Illustrative well operations include, but are not limited to, hydraulicfracturing, stimulation, tracer injection, cleaning, acidizing, steaminjection, water flooding, cementing, etc.

While embodiments described herein have been described with reference tovarious embodiments, it will be understood that various changes may bemade, and equivalents may be substituted for elements thereof withoutdeparting from the scope of the present disclosure. In addition, manymodifications will be appreciated to adapt a particular instrument,situation, or material to the teachings of the present disclosurewithout departing from the scope thereof. Therefore, it is intended thatthe disclosure is not limited to the particular embodiments disclosed asthe best mode contemplated for carrying the described features, but thatthe present disclosure will include all embodiments falling within thescope of the appended claims.

Accordingly, embodiments of the present disclosure are not to be seen aslimited by the foregoing description but are only limited by the scopeof the appended claims.

What is claimed is:
 1. A system for damping high frequency torsionaloscillations (HFTO) of a downhole system, the downhole systemcomprising: a drilling system disposed at an end of the downhole systemin operative connection with a drill bit; a damping system installed onthe drilling system, the damping system comprising at least one damperelement configured to dampen at least one HFTO mode; and at least onemode-shape tuning element arranged on the drilling system; wherein theat least one mode-shape tuning element is configured and positioned onthe drilling system to modify at least one of a shape of the at leastone HFTO mode, a frequency of the at least one HFTO mode, anexcitability of the at least one HFTO mode, and a damping efficiency ofthe at least one damper element.
 2. The system of claim 1, wherein theat least one mode-shape tuning element is configured and positioned onthe drilling system to modify the shape of the at least one HFTO mode ata position of the at least one damper element.
 3. The system of claim 1,wherein the at least one mode-shape tuning element is selected based onat least one of a dimension of the at least one mode-shape tuningelement, a material property of the at least one mode-shape tuningelement, and a mechanical property of the at least one mode-shape tuningelement.
 4. The system of claim 1, wherein the positioning of the atleast one mode-shape tuning element on the drilling system is selectedto at least one of modify the shape of the at least one HFTO mode at aposition of the at least one damper element and optimize the dampingefficiency of the at least one damper element.
 5. The system of claim 1,further comprising a pool of mode-shape tuning elements from which theat least one mode-shape tuning element is selected for arrangement onthe drilling system.
 6. The system of claim 1, wherein the at least onemode-shape tuning element is selected for arrangement on the drillingsystem based on a numeric simulation of the at least one HFTO of atleast a portion of the downhole system.
 7. The system of claim 6,wherein at least one of the at least one damper element and the at leastone mode-shape tuning element is positioned and/or selected based on anumeric inversion.
 8. The system of claim 1, wherein the damping systemis at least one of a viscous damping system, a friction damping system,a hydraulic damping system, a magnetic damping system, and apiezoelectric damping system.
 9. The system of claim 1, furthercomprising an isolator.
 10. The system of claim 1, wherein the at leastone damper element is arranged within 10 m of the drill bit.
 11. Amethod for damping high frequency torsional oscillations (HFTO) of adownhole system, the method comprising: drilling with a drilling systeminto the earth's subsurface, wherein the drilling system is in operativeconnection with a drill bit and comprises a damping system that includesat least one damper element and at least one mode-shape tuning elementarranged on the drilling system; configuring and positioning the atleast one mode-shape tuning element on the drilling system to modify atleast one of a shape of an HFTO mode, a frequency of the HFTO mode, anexcitability of the HFTO mode, and a damping efficiency of the at leastone damper element; and damping the HFTO mode with the at least onedamper element.
 12. The method of claim 11, wherein the at least onemode-shape tuning element is configured and positioned on the drillingsystem to modify the shape of the HFTO mode at a position of the atleast one damper element.
 13. The method of claim 11, further comprisingselecting the at least one mode-shape tuning element for the arrangementin the drilling system based on at least one of a dimension of the atleast one mode-shape tuning element, a material property of the at leastone mode-shape tuning element, and a mechanical property of the at leastone mode-shape tuning element.
 14. The method of claim 11, furthercomprising selecting a position of the at least one mode-shape tuningelement on the drilling system to at least one of modify the shape ofthe HFTO mode at a position of the at least one damper element andoptimize the damping efficiency of the at least one damper element. 15.The method of claim 11, further comprising selecting the at least onemode-shape tuning element from a pool of mode-shape tuning elements forthe arrangement in the drilling system.
 16. The method of claim 11,further comprising: executing a numeric simulation of the HFTO of atleast a portion of the downhole system; and selecting the at least onemode-shape tuning element for the arrangement in the drilling systembased on the numeric simulation of the HFTO of the portion of thedownhole system.
 17. The method of claim 16, further comprising:executing a numeric inversion; and at least one of positioning andselecting at least one of the at least one damper element and the atleast one mode-shape tuning element based on the numeric inversion. 18.The method of claim 11, wherein the damping system is at least one of aviscous damping system, a friction damping system, a hydraulic dampingsystem, a magnetic damping system, and a piezoelectric damping system.19. The method of claim 11, wherein the drilling system furthercomprises an isolator.
 20. The method of claim 11, wherein the at leastone damper element is arranged within 10 m of the drill bit.